The Binomial Probability Distribution
Many probability experiments have only two outcomes. For example, when you guess at a multiple choice question, your answer is either right or wrong. A medical treatment can be considered effective or ineffective. When a coin is tossed it can land either heads or tails. Situations like these are called binomial experiments.
Binomial experiments have the following properties:
- The procedure has a fixed number of trials.
- The trials must be independent. (The outcome of any individual trial doesn’t affect the probabilities in the other trials.)
- Each trial must have only two possible outcomes (commonly referred to as success and failure).
- The probability of a success remains the same in all trials.
The outcomes of a binomial experiment and the corresponding probabilities of these outcomes are called a binomial probability distribution.
Notation for Binomial Probability Distributions:
- $n$ denotes the fixed number of trials.
- $x$ denotes a specific number of successes in $n$ trials, so $x$ can be any whole number between 0 and $n$, inclusive.
- $p$ denotes the probability of success in one of the $n$ trials.
- $q$ denotes the probability of failure in one of the $n$ trials.
- $P(x)$ denotes the probability of getting exactly $x$ successes among the $n$ trials.
The Binomial
Probability Formula
\[
P(x)=\big(\, _nC_x\big)\cdot p^x\cdot q^{n-x}
\] for $x=0, 1, 2, ... , n$, and recall that $_nC_x=\frac{n!}{(n-x)!\cdot x!}$.
Example: Assume that a procedure yields a binomial probability model with a trial repeated $n=6$ times. Suppose the probability of success on a single trial is $p=0.40$.
Then, the probability model can be described with either the Binomial Formula, a table or a probability histogram.
$$
\begin{align*}
&P(X=x)\\[0.1in]
&=\big(\, _nC_x\big)\cdot p^x\cdot q^{n-x} \\[0.1in]
& =\big(\, _6C_x\big)\cdot (0.4)^x\cdot (0.6)^{6-x}
\end{align*}
$$
$$
\begin{array}{|c|c|}\hline
x & P(X=x)\\ \hline
0 & 0.047 \\
1 & 0.187 \\
2 & 0.311 \\
3 & 0.276 \\
4 & 0.138 \\
5 & 0.037 \\
6 & 0.004 \\
\hline
\end{array}
$$
'
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
2& 0 & & 0.9801&0.9025&0.8100&0.7225&0.6400&0.5625&0.4900&0.4444&0.4225&0.3600&0.3025\\
& 1 & & 0.0198&0.0950&0.1800&0.2550&0.3200&0.3750&0.4200&0.4444&0.4550&0.4800&0.4950\\
& 2 & & 0.0001&0.0025&0.0100&0.0225&0.0400&0.0625&0.0900&0.1111&0.1225&0.1600&0.2025\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 2& 0& &0.2500& 0.2025&0.1600&0.1225&0.1111&0.0900&0.0625&0.0400&0.0225&0.0100&0.0025\\ & 1& &0.5000& 0.4950&0.4800&0.4550&0.4444&0.4200&0.3750&0.3200&0.2550&0.1800&0.0950\\ & 2& &0.2500& 0.3025&0.3600&0.4225&0.4444&0.4900&0.5625&0.6400&0.7225&0.8100&0.9025\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 2& 0& &0.2500& 0.2025&0.1600&0.1225&0.1111&0.0900&0.0625&0.0400&0.0225&0.0100&0.0025\\ & 1& &0.5000& 0.4950&0.4800&0.4550&0.4444&0.4200&0.3750&0.3200&0.2550&0.1800&0.0950\\ & 2& &0.2500& 0.3025&0.3600&0.4225&0.4444&0.4900&0.5625&0.6400&0.7225&0.8100&0.9025\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
3& 0& & 0.9703&0.8574&0.7290&0.6141&0.5120&0.4219&0.3430&0.2963&0.2746&0.2160&0.1664\\
& 1& & 0.0294&0.1354&0.2430&0.3251&0.3840&0.4219&0.4410&0.4444&0.4436&0.4320&0.4084\\
& 2& & 0.0003&0.0071&0.0270&0.0574&0.0960&0.1406&0.1890&0.2222&0.2389&0.2880&0.3341\\
& 3& & \phantom{0}&0.0001&0.0010&0.0034&0.0080&0.0156&0.0270&0.0370&0.0429&0.0640&0.0911\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 3& 0& & 0.1250&0.0911&0.0640&0.0429&0.0370&0.0270&0.0156&0.0080&0.0034&0.0010&0.0001\\ & 1& & 0.3750&0.3341&0.2880&0.2389&0.2222&0.1890&0.1406&0.0960&0.0574&0.0270&0.0071\\ & 2& & 0.3750&0.4084&0.4320&0.4436&0.4444&0.4410&0.4219&0.3840&0.3251&0.2430&0.1354\\ & 3& & 0.1250&0.1664&0.2160&0.2746&0.2963&0.3430&0.4219&0.5120&0.6141&0.7290&0.8574\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 3& 0& & 0.1250&0.0911&0.0640&0.0429&0.0370&0.0270&0.0156&0.0080&0.0034&0.0010&0.0001\\ & 1& & 0.3750&0.3341&0.2880&0.2389&0.2222&0.1890&0.1406&0.0960&0.0574&0.0270&0.0071\\ & 2& & 0.3750&0.4084&0.4320&0.4436&0.4444&0.4410&0.4219&0.3840&0.3251&0.2430&0.1354\\ & 3& & 0.1250&0.1664&0.2160&0.2746&0.2963&0.3430&0.4219&0.5120&0.6141&0.7290&0.8574\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
4& 0& & 0.9606&0.8145&0.6561&0.5220&0.4096&0.3164&0.2401&0.1975&0.1785&0.1296&0.0915\\
& 1& & 0.0388&0.1715&0.2916&0.3685&0.4096&0.4219&0.4116&0.3951&0.3845&0.3456&0.2995\\
& 2& & 0.0006&0.0135&0.0486&0.0975&0.1536&0.2109&0.2646&0.2963&0.3105&0.3456&0.3675\\
& 3& & \phantom{0}&0.0005&0.0036&0.0115&0.0256&0.0469&0.0756&0.0988&0.1115&0.1536&0.2005\\
& 4& & \phantom{0}&\phantom{0}&0.0001&0.0005&0.0016&0.0039&0.0081&0.0123&0.0150&0.0256&0.0410\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 4& 0& & 0.0625&0.0410&0.0256&0.0150&0.0123&0.0081&0.0039&0.0016&0.0005&0.0001&\phantom{0}\\ & 1& & 0.2500&0.2005&0.1536&0.1115&0.0988&0.0756&0.0469&0.0256&0.0115&0.0036&0.0005\\ & 2& & 0.3750&0.3675&0.3456&0.3105&0.2963&0.2646&0.2109&0.1536&0.0975&0.0486&0.0135\\ & 3& & 0.2500&0.2995&0.3456&0.3845&0.3951&0.4116&0.4219&0.4096&0.3685&0.2916&0.1715\\ & 4& & 0.0625&0.0915&0.1296&0.1785&0.1975&0.2401&0.3164&0.4096&0.5220&0.6561&0.8145\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 4& 0& & 0.0625&0.0410&0.0256&0.0150&0.0123&0.0081&0.0039&0.0016&0.0005&0.0001&\phantom{0}\\ & 1& & 0.2500&0.2005&0.1536&0.1115&0.0988&0.0756&0.0469&0.0256&0.0115&0.0036&0.0005\\ & 2& & 0.3750&0.3675&0.3456&0.3105&0.2963&0.2646&0.2109&0.1536&0.0975&0.0486&0.0135\\ & 3& & 0.2500&0.2995&0.3456&0.3845&0.3951&0.4116&0.4219&0.4096&0.3685&0.2916&0.1715\\ & 4& & 0.0625&0.0915&0.1296&0.1785&0.1975&0.2401&0.3164&0.4096&0.5220&0.6561&0.8145\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
5& 0& & 0.9510&0.7738&0.5905&0.4437&0.3277&0.2373&0.1681&0.1317&0.1160&0.0778&0.0503\\
& 1& & 0.0480&0.2036&0.3280&0.3915&0.4096&0.3955&0.3601&0.3292&0.3124&0.2592&0.2059\\
& 2& & 0.0010&0.0214&0.0729&0.1382&0.2048&0.2637&0.3087&0.3292&0.3364&0.3456&0.3369\\
& 3& & \phantom{0}&0.0011&0.0081&0.0244&0.0512&0.0879&0.1323&0.1646&0.1811&0.2304&0.2757\\
& 4& & \phantom{0}&\phantom{0}&0.0005&0.0022&0.0064&0.0146&0.0283&0.0412&0.0488&0.0768&0.1128\\
& 5& & \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0010&0.0024&0.0041&0.0053&0.0102&0.0185\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 5& 0& & 0.0312&0.0185&0.0102&0.0053&0.0041&0.0024&0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}\\ & 1& & 0.1562&0.1128&0.0768&0.0488&0.0412&0.0283&0.0146&0.0064&0.0022&0.0004&\phantom{0}\\ & 2& & 0.3125&0.2757&0.2304&0.1811&0.1646&0.1323&0.0879&0.0512&0.0244&0.0081&0.0011\\ & 3& & 0.3125&0.3369&0.3456&0.3364&0.3292&0.3087&0.2637&0.2048&0.1382&0.0729&0.0214\\ & 4& & 0.1562&0.2059&0.2592&0.3124&0.3292&0.3601&0.3955&0.4096&0.3915&0.3280&0.2036\\ & 5& & 0.0312&0.0503&0.0778&0.1160&0.1317&0.1681&0.2373&0.3277&0.4437&0.5905&0.7738\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 5& 0& & 0.0312&0.0185&0.0102&0.0053&0.0041&0.0024&0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}\\ & 1& & 0.1562&0.1128&0.0768&0.0488&0.0412&0.0283&0.0146&0.0064&0.0022&0.0004&\phantom{0}\\ & 2& & 0.3125&0.2757&0.2304&0.1811&0.1646&0.1323&0.0879&0.0512&0.0244&0.0081&0.0011\\ & 3& & 0.3125&0.3369&0.3456&0.3364&0.3292&0.3087&0.2637&0.2048&0.1382&0.0729&0.0214\\ & 4& & 0.1562&0.2059&0.2592&0.3124&0.3292&0.3601&0.3955&0.4096&0.3915&0.3280&0.2036\\ & 5& & 0.0312&0.0503&0.0778&0.1160&0.1317&0.1681&0.2373&0.3277&0.4437&0.5905&0.7738\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
6& 0& & 0.9415&0.7351&0.5314&0.3771&0.2621&0.1780&0.1176&0.0878&0.0754&0.0467&0.0277\\
& 1& & 0.0571&0.2321&0.3543&0.3993&0.3932&0.3560&0.3025&0.2634&0.2437&0.1866&0.1359\\
& 2& & 0.0014&0.0305&0.0984&0.1762&0.2458&0.2966&0.3241&0.3292&0.3280&0.3110&0.2780\\
& 3& & \phantom{0}&0.0021&0.0146&0.0415&0.0819&0.1318&0.1852&0.2195&0.2355&0.2765&0.3032\\
& 4& & \phantom{0}&0.0001&0.0012&0.0055&0.0154&0.0330&0.0595&0.0823&0.0951&0.1382&0.1861\\
& 5& & \phantom{0}&\phantom{0}&0.0001&0.0004&0.0015&0.0044&0.0102&0.0165&0.0205&0.0369&0.0609\\
& 6& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0007&0.0014&0.0018&0.0041&0.0083\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 6& 0& & 0.0156&0.0083&0.0041&0.0018&0.0014&0.0007&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0938&0.0609&0.0369&0.0205&0.0165&0.0102&0.0044&0.0015&0.0004&0.0001&\phantom{0}\\ & 2& & 0.2344&0.1861&0.1382&0.0951&0.0823&0.0595&0.0330&0.0154&0.0055&0.0012&0.0001\\ & 3& & 0.3125&0.3032&0.2765&0.2355&0.2195&0.1852&0.1318&0.0819&0.0415&0.0146&0.0021\\ & 4& & 0.2344&0.2780&0.3110&0.3280&0.3292&0.3241&0.2966&0.2458&0.1762&0.0984&0.0305\\ & 5& & 0.0938&0.1359&0.1866&0.2437&0.2634&0.3025&0.3560&0.3932&0.3993&0.3543&0.2321\\ & 6& & 0.0156&0.0277&0.0467&0.0754&0.0878&0.1176&0.1780&0.2621&0.3771&0.5314&0.7351\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 6& 0& & 0.0156&0.0083&0.0041&0.0018&0.0014&0.0007&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0938&0.0609&0.0369&0.0205&0.0165&0.0102&0.0044&0.0015&0.0004&0.0001&\phantom{0}\\ & 2& & 0.2344&0.1861&0.1382&0.0951&0.0823&0.0595&0.0330&0.0154&0.0055&0.0012&0.0001\\ & 3& & 0.3125&0.3032&0.2765&0.2355&0.2195&0.1852&0.1318&0.0819&0.0415&0.0146&0.0021\\ & 4& & 0.2344&0.2780&0.3110&0.3280&0.3292&0.3241&0.2966&0.2458&0.1762&0.0984&0.0305\\ & 5& & 0.0938&0.1359&0.1866&0.2437&0.2634&0.3025&0.3560&0.3932&0.3993&0.3543&0.2321\\ & 6& & 0.0156&0.0277&0.0467&0.0754&0.0878&0.1176&0.1780&0.2621&0.3771&0.5314&0.7351\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
7& 0& & 0.9321&0.6983&0.4783&0.3206&0.2097&0.1335&0.0824&0.0585&0.0490&0.0280&0.0152\\
& 1& & 0.0659&0.2573&0.3720&0.3960&0.3670&0.3115&0.2471&0.2048&0.1848&0.1306&0.0872\\
& 2& & 0.0020&0.0406&0.1240&0.2097&0.2753&0.3115&0.3177&0.3073&0.2985&0.2613&0.2140\\
& 3& & \phantom{0}&0.0036&0.0230&0.0617&0.1147&0.1730&0.2269&0.2561&0.2679&0.2903&0.2918\\
& 4& & \phantom{0}&0.0002&0.0026&0.0109&0.0287&0.0577&0.0972&0.1280&0.1442&0.1935&0.2388\\
& 5& & \phantom{0}&\phantom{0}&0.0002&0.0012&0.0043&0.0115&0.0250&0.0384&0.0466&0.0774&0.1172\\
& 6& & \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0004&0.0013&0.0036&0.0064&0.0084&0.0172&0.0320\\
& 7& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0005&0.0006&0.0016&0.0037\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 7& 0& & 0.0078&0.0037&0.0016&0.0006&0.0005&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0547&0.0320&0.0172&0.0084&0.0064&0.0036&0.0013&0.0004&0.0001&\phantom{0}&\phantom{0}\\ & 2& & 0.1641&0.1172&0.0774&0.0466&0.0384&0.0250&0.0115&0.0043&0.0012&0.0002&\phantom{0}\\ & 3& & 0.2734&0.2388&0.1935&0.1442&0.1280&0.0972&0.0577&0.0287&0.0109&0.0026&0.0002\\ & 4& & 0.2734&0.2918&0.2903&0.2679&0.2561&0.2269&0.1730&0.1147&0.0617&0.0230&0.0036\\ & 5& & 0.1641&0.2140&0.2613&0.2985&0.3073&0.3177&0.3115&0.2753&0.2097&0.1240&0.0406\\ &6 & & 0.0547&0.0872&0.1306&0.1848&0.2048&0.2471&0.3115&0.3670&0.3960&0.3720&0.2573\\ & 7& & 0.0078&0.0152&0.0280&0.0490&0.0585&0.0824&0.1335&0.2097&0.3206&0.4783&0.6983\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 7& 0& & 0.0078&0.0037&0.0016&0.0006&0.0005&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0547&0.0320&0.0172&0.0084&0.0064&0.0036&0.0013&0.0004&0.0001&\phantom{0}&\phantom{0}\\ & 2& & 0.1641&0.1172&0.0774&0.0466&0.0384&0.0250&0.0115&0.0043&0.0012&0.0002&\phantom{0}\\ & 3& & 0.2734&0.2388&0.1935&0.1442&0.1280&0.0972&0.0577&0.0287&0.0109&0.0026&0.0002\\ & 4& & 0.2734&0.2918&0.2903&0.2679&0.2561&0.2269&0.1730&0.1147&0.0617&0.0230&0.0036\\ & 5& & 0.1641&0.2140&0.2613&0.2985&0.3073&0.3177&0.3115&0.2753&0.2097&0.1240&0.0406\\ &6 & & 0.0547&0.0872&0.1306&0.1848&0.2048&0.2471&0.3115&0.3670&0.3960&0.3720&0.2573\\ & 7& & 0.0078&0.0152&0.0280&0.0490&0.0585&0.0824&0.1335&0.2097&0.3206&0.4783&0.6983\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
8& 0& & 0.9227&0.6634&0.4305&0.2725&0.1678&0.1001&0.0576&0.0390&0.0319&0.0168&0.0084\\
& 1& & 0.0746&0.2793&0.3826&0.3847&0.3355&0.2670&0.1977&0.1561&0.1373&0.0896&0.0548\\
& 2& & 0.0026&0.0515&0.1488&0.2376&0.2936&0.3115&0.2965&0.2731&0.2587&0.2090&0.1569\\
& 3& & 0.0001&0.0054&0.0331&0.0839&0.1468&0.2076&0.2541&0.2731&0.2786&0.2787&0.2568\\
& 4& & \phantom{0}&0.0004&0.0046&0.0185&0.0459&0.0865&0.1361&0.1707&0.1875&0.2322&0.2627\\
& 5& & \phantom{0}&\phantom{0}&0.0004&0.0026&0.0092&0.0231&0.0467&0.0683&0.0808&0.1239&0.1719\\
& 6& & \phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0011&0.0038&0.0100&0.0171&0.0217&0.0413&0.0703\\
& 7& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0004&0.0012&0.0024&0.0033&0.0079&0.0164\\
& 8& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0002&0.0007&0.0017\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 8& 0& & 0.0039&0.0017&0.0007&0.0002&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0312&0.0164&0.0079&0.0033&0.0024&0.0012&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.1094&0.0703&0.0413&0.0217&0.0171&0.0100&0.0038&0.0011&0.0002&\phantom{0}&\phantom{0}\\ & 3& & 0.2187&0.1719&0.1239&0.0808&0.0683&0.0467&0.0231&0.0092&0.0026&0.0004&\phantom{0}\\ & 4& & 0.2734&0.2627&0.2322&0.1875&0.1707&0.1361&0.0865&0.0459&0.0185&0.0046&0.0004\\ & 5& & 0.2187&0.2568&0.2787&0.2786&0.2731&0.2541&0.2076&0.1468&0.0839&0.0331&0.0054\\ & 6& & 0.1094&0.1569&0.2090&0.2587&0.2731&0.2965&0.3115&0.2936&0.2376&0.1488&0.0515\\ & 7& & 0.0312&0.0548&0.0896&0.1373&0.1561&0.1977&0.2670&0.3355&0.3847&0.3826&0.2793\\ & 8& & 0.0039&0.0084&0.0168&0.0319&0.0390&0.0576&0.1001&0.1678&0.2725&0.4305&0.6634\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 8& 0& & 0.0039&0.0017&0.0007&0.0002&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0312&0.0164&0.0079&0.0033&0.0024&0.0012&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.1094&0.0703&0.0413&0.0217&0.0171&0.0100&0.0038&0.0011&0.0002&\phantom{0}&\phantom{0}\\ & 3& & 0.2187&0.1719&0.1239&0.0808&0.0683&0.0467&0.0231&0.0092&0.0026&0.0004&\phantom{0}\\ & 4& & 0.2734&0.2627&0.2322&0.1875&0.1707&0.1361&0.0865&0.0459&0.0185&0.0046&0.0004\\ & 5& & 0.2187&0.2568&0.2787&0.2786&0.2731&0.2541&0.2076&0.1468&0.0839&0.0331&0.0054\\ & 6& & 0.1094&0.1569&0.2090&0.2587&0.2731&0.2965&0.3115&0.2936&0.2376&0.1488&0.0515\\ & 7& & 0.0312&0.0548&0.0896&0.1373&0.1561&0.1977&0.2670&0.3355&0.3847&0.3826&0.2793\\ & 8& & 0.0039&0.0084&0.0168&0.0319&0.0390&0.0576&0.1001&0.1678&0.2725&0.4305&0.6634\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
9& 0& & 0.9135&0.6302&0.3874&0.2316&0.1342&0.0751&0.0404&0.0260&0.0207&0.0101&0.0046\\
& 1& & 0.0830&0.2985&0.3874&0.3679&0.3020&0.2253&0.1556&0.1171&0.1004&0.0605&0.0339\\
& 2& & 0.0034&0.0629&0.1722&0.2597&0.3020&0.3003&0.2668&0.2341&0.2162&0.1612&0.1110\\
& 3& & 0.0001&0.0077&0.0446&0.1069&0.1762&0.2336&0.2668&0.2731&0.2716&0.2508&0.2119\\
& 4& & \phantom{0}&0.0006&0.0074&0.0283&0.0661&0.1168&0.1715&0.2048&0.2194&0.2508&0.2600\\
& 5& & \phantom{0}&\phantom{0}&0.0008&0.0050&0.0165&0.0389&0.0735&0.1024&0.1181&0.1672&0.2128\\
& 6& & \phantom{0}&\phantom{0}&0.0001&0.0006&0.0028&0.0087&0.0210&0.0341&0.0424&0.0743&0.1160\\
& 7& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0003&0.0012&0.0039&0.0073&0.0098&0.0212&0.0407\\
&8 & & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0004&0.0009&0.0013&0.0035&0.0083\\
& 9& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0003&0.0008\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 9& 0& & 0.0020&0.0008&0.0003&0.0001&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0176&0.0083&0.0035&0.0013&0.0009&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0703&0.0407&0.0212&0.0098&0.0073&0.0039&0.0012&0.0003&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.1641&0.1160&0.0743&0.0424&0.0341&0.0210&0.0087&0.0028&0.0006&0.0001&\phantom{0}\\ &4 & & 0.2461&0.2128&0.1672&0.1181&0.1024&0.0735&0.0389&0.0165&0.0050&0.0008&\phantom{0}\\ & 5& & 0.2461&0.2600&0.2508&0.2194&0.2048&0.1715&0.1168&0.0661&0.0283&0.0074&0.0006\\ & 6& & 0.1641&0.2119&0.2508&0.2716&0.2731&0.2668&0.2336&0.1762&0.1069&0.0446&0.0077\\ & 7& & 0.0703&0.1110&0.1612&0.2162&0.2341&0.2668&0.3003&0.3020&0.2597&0.1722&0.0629\\ &8& & 0.0176&0.0339&0.0605&0.1004&0.1171&0.1556&0.2253&0.3020&0.3679&0.3874&0.2985\\ & 9& & 0.0020&0.0046&0.0101&0.0207&0.0260&0.0404&0.0751&0.1342&0.2316&0.3874&0.6302\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 9& 0& & 0.0020&0.0008&0.0003&0.0001&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0176&0.0083&0.0035&0.0013&0.0009&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0703&0.0407&0.0212&0.0098&0.0073&0.0039&0.0012&0.0003&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.1641&0.1160&0.0743&0.0424&0.0341&0.0210&0.0087&0.0028&0.0006&0.0001&\phantom{0}\\ &4 & & 0.2461&0.2128&0.1672&0.1181&0.1024&0.0735&0.0389&0.0165&0.0050&0.0008&\phantom{0}\\ & 5& & 0.2461&0.2600&0.2508&0.2194&0.2048&0.1715&0.1168&0.0661&0.0283&0.0074&0.0006\\ & 6& & 0.1641&0.2119&0.2508&0.2716&0.2731&0.2668&0.2336&0.1762&0.1069&0.0446&0.0077\\ & 7& & 0.0703&0.1110&0.1612&0.2162&0.2341&0.2668&0.3003&0.3020&0.2597&0.1722&0.0629\\ &8& & 0.0176&0.0339&0.0605&0.1004&0.1171&0.1556&0.2253&0.3020&0.3679&0.3874&0.2985\\ & 9& & 0.0020&0.0046&0.0101&0.0207&0.0260&0.0404&0.0751&0.1342&0.2316&0.3874&0.6302\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
10& 0& & 0.9044&0.5987&0.3487&0.1969&0.1074&0.0563&0.0282&0.0173&0.0135&0.0060&0.0025\\
& 1& & 0.0914&0.3151&0.3874&0.3474&0.2684&0.1877&0.1211&0.0867&0.0725&0.0403&0.0207\\
& 2& & 0.0042&0.0746&0.1937&0.2759&0.3020&0.2816&0.2335&0.1951&0.1757&0.1209&0.0763\\
&3 & & 0.0001&0.0105&0.0574&0.1298&0.2013&0.2503&0.2668&0.2601&0.2522&0.2150&0.1665\\
& 4& & \phantom{0}&0.0010&0.0112&0.0401&0.0881&0.1460&0.2001&0.2276&0.2377&0.2508&0.2384\\
&5& & \phantom{0}&0.0001&0.0015&0.0085&0.0264&0.0584&0.1029&0.1366&0.1536&0.2007&0.2340\\
&6 & & \phantom{0}&\phantom{0}&0.0001&0.0012&0.0055&0.0162&0.0368&0.0569&0.0689&0.1115&0.1596\\
&7& & \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0008&0.0031&0.0090&0.0163&0.0212&0.0425&0.0746\\
& 8& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0004&0.0014&0.0030&0.0043&0.0106&0.0229\\
&9 & & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0005&0.0016&0.0042\\
& 10& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 10&0 & & 0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0098&0.0042&0.0016&0.0005&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0439&0.0229&0.0106&0.0043&0.0030&0.0014&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ &3& & 0.1172&0.0746&0.0425&0.0212&0.0163&0.0090&0.0031&0.0008&0.0001&\phantom{0}&\phantom{0}\\ & 4& & 0.2051&0.1596&0.1115&0.0689&0.0569&0.0368&0.0162&0.0055&0.0012&0.0001&\phantom{0}\\ & 5& & 0.2461&0.2340&0.2007&0.1536&0.1366&0.1029&0.0584&0.0264&0.0085&0.0015&0.0001\\ &6 & & 0.2051&0.2384&0.2508&0.2377&0.2276&0.2001&0.1460&0.0881&0.0401&0.0112&0.0010\\ &7 & & 0.1172&0.1665&0.2150&0.2522&0.2601&0.2668&0.2503&0.2013&0.1298&0.0574&0.0105\\ &8 & & 0.0439&0.0763&0.1209&0.1757&0.1951&0.2335&0.2816&0.3020&0.2759&0.1937&0.0746\\ &9 & & 0.0098&0.0207&0.0403&0.0725&0.0867&0.1211&0.1877&0.2684&0.3474&0.3874&0.3151\\ &10 & & 0.0010&0.0025&0.0060&0.0135&0.0173&0.0282&0.0563&0.1074&0.1969&0.3487&0.5987\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 10&0 & & 0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0098&0.0042&0.0016&0.0005&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0439&0.0229&0.0106&0.0043&0.0030&0.0014&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ &3& & 0.1172&0.0746&0.0425&0.0212&0.0163&0.0090&0.0031&0.0008&0.0001&\phantom{0}&\phantom{0}\\ & 4& & 0.2051&0.1596&0.1115&0.0689&0.0569&0.0368&0.0162&0.0055&0.0012&0.0001&\phantom{0}\\ & 5& & 0.2461&0.2340&0.2007&0.1536&0.1366&0.1029&0.0584&0.0264&0.0085&0.0015&0.0001\\ &6 & & 0.2051&0.2384&0.2508&0.2377&0.2276&0.2001&0.1460&0.0881&0.0401&0.0112&0.0010\\ &7 & & 0.1172&0.1665&0.2150&0.2522&0.2601&0.2668&0.2503&0.2013&0.1298&0.0574&0.0105\\ &8 & & 0.0439&0.0763&0.1209&0.1757&0.1951&0.2335&0.2816&0.3020&0.2759&0.1937&0.0746\\ &9 & & 0.0098&0.0207&0.0403&0.0725&0.0867&0.1211&0.1877&0.2684&0.3474&0.3874&0.3151\\ &10 & & 0.0010&0.0025&0.0060&0.0135&0.0173&0.0282&0.0563&0.1074&0.1969&0.3487&0.5987\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
11& 0& & 0.8953&0.5688&0.3138&0.1673&0.0859&0.0422&0.0198&0.0116&0.0088&0.0036&0.0014\\
& 1& & 0.0995&0.3293&0.3835&0.3248&0.2362&0.1549&0.0932&0.0636&0.0518&0.0266&0.0125\\
& 2& & 0.0050&0.0867&0.2131&0.2866&0.2953&0.2581&0.1998&0.1590&0.1395&0.0887&0.0513\\
& 3& & 0.0002&0.0137&0.0710&0.1517&0.2215&0.2581&0.2568&0.2384&0.2254&0.1774&0.1259\\
& 4& & \phantom{0}&0.0014&0.0158&0.0536&0.1107&0.1721&0.2201&0.2384&0.2428&0.2365&0.2060\\
& 5& & \phantom{0}&0.0001&0.0025&0.0132&0.0388&0.0803&0.1321&0.1669&0.1830&0.2207&0.2360\\
& 6& & \phantom{0}&\phantom{0}&0.0003&0.0023&0.0097&0.0268&0.0566&0.0835&0.0985&0.1471&0.1931\\
& 7& & \phantom{0}&\phantom{0}&\phantom{0}&0.0003&0.0017&0.0064&0.0173&0.0298&0.0379&0.0701&0.1128\\
& 8& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0011&0.0037&0.0075&0.0102&0.0234&0.0462\\
& 9& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0005&0.0012&0.0018&0.0052&0.0126\\
& 10& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0007&0.0021\\
& 11& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 11&0 & & 0.0005&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0054&0.0021&0.0007&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0269&0.0126&0.0052&0.0018&0.0012&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ &3 & & 0.0806&0.0462&0.0234&0.0102&0.0075&0.0037&0.0011&0.0002&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.1611&0.1128&0.0701&0.0379&0.0298&0.0173&0.0064&0.0017&0.0003&\phantom{0}&\phantom{0}\\ &5 & & 0.2256&0.1931&0.1471&0.0985&0.0835&0.0566&0.0268&0.0097&0.0023&0.0003&\phantom{0}\\ & 6& & 0.2256&0.2360&0.2207&0.1830&0.1669&0.1321&0.0803&0.0388&0.0132&0.0025&0.0001\\ & 7& & 0.1611&0.2060&0.2365&0.2428&0.2384&0.2201&0.1721&0.1107&0.0536&0.0158&0.0014\\ &8 & & 0.0806&0.1259&0.1774&0.2254&0.2384&0.2568&0.2581&0.2215&0.1517&0.0710&0.0137\\ & 9& & 0.0269&0.0513&0.0887&0.1395&0.1590&0.1998&0.2581&0.2953&0.2866&0.2131&0.0867\\ & 10& & 0.0054&0.0125&0.0266&0.0518&0.0636&0.0932&0.1549&0.2362&0.3248&0.3835&0.3293\\ & 11& & 0.0005&0.0014&0.0036&0.0088&0.0116&0.0198&0.0422&0.0859&0.1673&0.3138&0.5688\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 11&0 & & 0.0005&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0054&0.0021&0.0007&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0269&0.0126&0.0052&0.0018&0.0012&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ &3 & & 0.0806&0.0462&0.0234&0.0102&0.0075&0.0037&0.0011&0.0002&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.1611&0.1128&0.0701&0.0379&0.0298&0.0173&0.0064&0.0017&0.0003&\phantom{0}&\phantom{0}\\ &5 & & 0.2256&0.1931&0.1471&0.0985&0.0835&0.0566&0.0268&0.0097&0.0023&0.0003&\phantom{0}\\ & 6& & 0.2256&0.2360&0.2207&0.1830&0.1669&0.1321&0.0803&0.0388&0.0132&0.0025&0.0001\\ & 7& & 0.1611&0.2060&0.2365&0.2428&0.2384&0.2201&0.1721&0.1107&0.0536&0.0158&0.0014\\ &8 & & 0.0806&0.1259&0.1774&0.2254&0.2384&0.2568&0.2581&0.2215&0.1517&0.0710&0.0137\\ & 9& & 0.0269&0.0513&0.0887&0.1395&0.1590&0.1998&0.2581&0.2953&0.2866&0.2131&0.0867\\ & 10& & 0.0054&0.0125&0.0266&0.0518&0.0636&0.0932&0.1549&0.2362&0.3248&0.3835&0.3293\\ & 11& & 0.0005&0.0014&0.0036&0.0088&0.0116&0.0198&0.0422&0.0859&0.1673&0.3138&0.5688\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
12& 0& & 0.8864&0.5404&0.2824&0.1422&0.0687&0.0317&0.0138&0.0077&0.0057&0.0022&0.0008\\
& 1& & 0.1074&0.3413&0.3766&0.3012&0.2062&0.1267&0.0712&0.0462&0.0368&0.0174&0.0075\\
& 2& & 0.0060&0.0988&0.2301&0.2924&0.2835&0.2323&0.1678&0.1272&0.1088&0.0639&0.0339\\
& 3& & 0.0002&0.0173&0.0852&0.1720&0.2362&0.2581&0.2397&0.2120&0.1954&0.1419&0.0923\\
& 4& & \phantom{0}&0.0021&0.0213&0.0683&0.1329&0.1936&0.2311&0.2384&0.2367&0.2128&0.1700\\
& 5& & \phantom{0}&0.0002&0.0038&0.0193&0.0532&0.1032&0.1585&0.1908&0.2039&0.2270&0.2225\\
& 6& & \phantom{0}&\phantom{0}&0.0005&0.0040&0.0155&0.0401&0.0792&0.1113&0.1281&0.1766&0.2124\\
& 7& & \phantom{0}&\phantom{0}&\phantom{0}&0.0006&0.0033&0.0115&0.0291&0.0477&0.0591&0.1009&0.1489\\
& 8& & \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0005&0.0024&0.0078&0.0149&0.0199&0.0420&0.0762\\
& 9& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0004&0.0015&0.0033&0.0048&0.0125&0.0277\\
& 10& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0005&0.0008&0.0025&0.0068\\
& 11& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0010\\
& 12& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 12& 0& & 0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0029&0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0161&0.0068&0.0025&0.0008&0.0005&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0537&0.0277&0.0125&0.0048&0.0033&0.0015&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.1208&0.0762&0.0420&0.0199&0.0149&0.0078&0.0024&0.0005&0.0001&\phantom{0}&\phantom{0}\\ & 5& & 0.1934&0.1489&0.1009&0.0591&0.0477&0.0291&0.0115&0.0033&0.0006&\phantom{0}&\phantom{0}\\ & 6& & 0.2256&0.2124&0.1766&0.1281&0.1113&0.0792&0.0401&0.0155&0.0040&0.0005&\phantom{0}\\ & 7& & 0.1934&0.2225&0.2270&0.2039&0.1908&0.1585&0.1032&0.0532&0.0193&0.0038&0.0002\\ & 8& & 0.1208&0.1700&0.2128&0.2367&0.2384&0.2311&0.1936&0.1329&0.0683&0.0213&0.0021\\ & 9& & 0.0537&0.0923&0.1419&0.1954&0.2120&0.2397&0.2581&0.2362&0.1720&0.0852&0.0173\\ & 10& & 0.0161&0.0339&0.0639&0.1088&0.1272&0.1678&0.2323&0.2835&0.2924&0.2301&0.0988\\ & 11& & 0.0029&0.0075&0.0174&0.0368&0.0462&0.0712&0.1267&0.2062&0.3012&0.3766&0.3413\\ & 12& & 0.0002&0.0008&0.0022&0.0057&0.0077&0.0138&0.0317&0.0687&0.1422&0.2824&0.5404\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 12& 0& & 0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0029&0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0161&0.0068&0.0025&0.0008&0.0005&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0537&0.0277&0.0125&0.0048&0.0033&0.0015&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.1208&0.0762&0.0420&0.0199&0.0149&0.0078&0.0024&0.0005&0.0001&\phantom{0}&\phantom{0}\\ & 5& & 0.1934&0.1489&0.1009&0.0591&0.0477&0.0291&0.0115&0.0033&0.0006&\phantom{0}&\phantom{0}\\ & 6& & 0.2256&0.2124&0.1766&0.1281&0.1113&0.0792&0.0401&0.0155&0.0040&0.0005&\phantom{0}\\ & 7& & 0.1934&0.2225&0.2270&0.2039&0.1908&0.1585&0.1032&0.0532&0.0193&0.0038&0.0002\\ & 8& & 0.1208&0.1700&0.2128&0.2367&0.2384&0.2311&0.1936&0.1329&0.0683&0.0213&0.0021\\ & 9& & 0.0537&0.0923&0.1419&0.1954&0.2120&0.2397&0.2581&0.2362&0.1720&0.0852&0.0173\\ & 10& & 0.0161&0.0339&0.0639&0.1088&0.1272&0.1678&0.2323&0.2835&0.2924&0.2301&0.0988\\ & 11& & 0.0029&0.0075&0.0174&0.0368&0.0462&0.0712&0.1267&0.2062&0.3012&0.3766&0.3413\\ & 12& & 0.0002&0.0008&0.0022&0.0057&0.0077&0.0138&0.0317&0.0687&0.1422&0.2824&0.5404\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
13& 0& & 0.8775&0.5133&0.2542&0.1209&0.0550&0.0238&0.0097&0.0051&0.0037&0.0013&0.0004\\
& 1& & 0.1152&0.3512&0.3672&0.2774&0.1787&0.1029&0.0540&0.0334&0.0259&0.0113&0.0045\\
& 2& & 0.0070&0.1109&0.2448&0.2937&0.2680&0.2059&0.1388&0.1002&0.0836&0.0453&0.0220\\
& 3& & 0.0003&0.0214&0.0997&0.1900&0.2457&0.2517&0.2181&0.1837&0.1651&0.1107&0.0660\\
& 4& & \phantom{0}&0.0028&0.0277&0.0838&0.1535&0.2097&0.2337&0.2296&0.2222&0.1845&0.1350\\
& 5& & \phantom{0}&0.0003&0.0055&0.0266&0.0691&0.1258&0.1803&0.2067&0.2154&0.2214&0.1989\\
& 6& & \phantom{0}&\phantom{0}&0.0008&0.0063&0.0230&0.0559&0.1030&0.1378&0.1546&0.1968&0.2169\\
& 7& & \phantom{0}&\phantom{0}&0.0001&0.0011&0.0058&0.0186&0.0442&0.0689&0.0833&0.1312&0.1775\\
& 8& & \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0011&0.0047&0.0142&0.0258&0.0336&0.0656&0.1089\\
& 9& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0009&0.0034&0.0072&0.0101&0.0243&0.0495\\
& 10& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0006&0.0014&0.0022&0.0065&0.0162\\
& 11& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0003&0.0012&0.0036\\
& 12& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0005\\
& 13& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 13& 0& & 0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0016&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0095&0.0036&0.0012&0.0003&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0349&0.0162&0.0065&0.0022&0.0014&0.0006&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0873&0.0495&0.0243&0.0101&0.0072&0.0034&0.0009&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.1571&0.1089&0.0656&0.0336&0.0258&0.0142&0.0047&0.0011&0.0001&\phantom{0}&\phantom{0}\\ & 6& & 0.2095&0.1775&0.1312&0.0833&0.0689&0.0442&0.0186&0.0058&0.0011&0.0001&\phantom{0}\\ & 7& & 0.2095&0.2169&0.1968&0.1546&0.1378&0.1030&0.0559&0.0230&0.0063&0.0008&\phantom{0}\\ & 8& & 0.1571&0.1989&0.2214&0.2154&0.2067&0.1803&0.1258&0.0691&0.0266&0.0055&0.0003\\ &9 & & 0.0873&0.1350&0.1845&0.2222&0.2296&0.2337&0.2097&0.1535&0.0838&0.0277&0.0028\\ & 10& & 0.0349&0.0660&0.1107&0.1651&0.1837&0.2181&0.2517&0.2457&0.1900&0.0997&0.0214\\ & 11& & 0.0095&0.0220&0.0453&0.0836&0.1002&0.1388&0.2059&0.2680&0.2937&0.2448&0.1109\\ & 12& & 0.0016&0.0045&0.0113&0.0259&0.0334&0.0540&0.1029&0.1787&0.2774&0.3672&0.3512\\ & 13& & 0.0001&0.0004&0.0013&0.0037&0.0051&0.0097&0.0238&0.0550&0.1209&0.2542&0.5133\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 13& 0& & 0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0016&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0095&0.0036&0.0012&0.0003&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0349&0.0162&0.0065&0.0022&0.0014&0.0006&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0873&0.0495&0.0243&0.0101&0.0072&0.0034&0.0009&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.1571&0.1089&0.0656&0.0336&0.0258&0.0142&0.0047&0.0011&0.0001&\phantom{0}&\phantom{0}\\ & 6& & 0.2095&0.1775&0.1312&0.0833&0.0689&0.0442&0.0186&0.0058&0.0011&0.0001&\phantom{0}\\ & 7& & 0.2095&0.2169&0.1968&0.1546&0.1378&0.1030&0.0559&0.0230&0.0063&0.0008&\phantom{0}\\ & 8& & 0.1571&0.1989&0.2214&0.2154&0.2067&0.1803&0.1258&0.0691&0.0266&0.0055&0.0003\\ &9 & & 0.0873&0.1350&0.1845&0.2222&0.2296&0.2337&0.2097&0.1535&0.0838&0.0277&0.0028\\ & 10& & 0.0349&0.0660&0.1107&0.1651&0.1837&0.2181&0.2517&0.2457&0.1900&0.0997&0.0214\\ & 11& & 0.0095&0.0220&0.0453&0.0836&0.1002&0.1388&0.2059&0.2680&0.2937&0.2448&0.1109\\ & 12& & 0.0016&0.0045&0.0113&0.0259&0.0334&0.0540&0.1029&0.1787&0.2774&0.3672&0.3512\\ & 13& & 0.0001&0.0004&0.0013&0.0037&0.0051&0.0097&0.0238&0.0550&0.1209&0.2542&0.5133\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
14& 0& & 0.8687&0.4877&0.2288&0.1028&0.0440&0.0178&0.0068&0.0034&0.0024&0.0008&0.0002\\
& 1& & 0.1229&0.3593&0.3559&0.2539&0.1539&0.0832&0.0407&0.0240&0.0181&0.0073&0.0027\\
& 2& & 0.0081&0.1229&0.2570&0.2912&0.2501&0.1802&0.1134&0.0779&0.0634&0.0317&0.0141\\
& 3& & 0.0003&0.0259&0.1142&0.2056&0.2501&0.2402&0.1943&0.1559&0.1366&0.0845&0.0462\\
& 4& & \phantom{0}&0.0037&0.0349&0.0998&0.1720&0.2202&0.2290&0.2143&0.2022&0.1549&0.1040\\
& 5& & \phantom{0}&0.0004&0.0078&0.0352&0.0860&0.1468&0.1963&0.2143&0.2178&0.2066&0.1701\\
& 6& & \phantom{0}&\phantom{0}&0.0013&0.0093&0.0322&0.0734&0.1262&0.1607&0.1759&0.2066&0.2088\\
& 7& & \phantom{0}&\phantom{0}&0.0002&0.0019&0.0092&0.0280&0.0618&0.0918&0.1082&0.1574&0.1952\\
& 8& & \phantom{0}&\phantom{0}&\phantom{0}&0.0003&0.0020&0.0082&0.0232&0.0402&0.0510&0.0918&0.1398\\
& 9& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0003&0.0018&0.0066&0.0134&0.0183&0.0408&0.0762\\
& 10& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0003&0.0014&0.0033&0.0049&0.0136&0.0312\\
& 11& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0006&0.0010&0.0033&0.0093\\
& 12& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0005&0.0019\\
& 13& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002\\
& 14& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 14& 0& & 0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0009&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0056&0.0019&0.0005&0.0001&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0222&0.0093&0.0033&0.0010&0.0006&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0611&0.0312&0.0136&0.0049&0.0033&0.0014&0.0003&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.1222&0.0762&0.0408&0.0183&0.0134&0.0066&0.0018&0.0003&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.1833&0.1398&0.0918&0.0510&0.0402&0.0232&0.0082&0.0020&0.0003&\phantom{0}&\phantom{0}\\ & 7& & 0.2095&0.1952&0.1574&0.1082&0.0918&0.0618&0.0280&0.0092&0.0019&0.0002&\phantom{0}\\ & 8& & 0.1833&0.2088&0.2066&0.1759&0.1607&0.1262&0.0734&0.0322&0.0093&0.0013&\phantom{0}\\ & 9& & 0.1222&0.1701&0.2066&0.2178&0.2143&0.1963&0.1468&0.0860&0.0352&0.0078&0.0004\\ & 10& & 0.0611&0.1040&0.1549&0.2022&0.2143&0.2290&0.2202&0.1720&0.0998&0.0349&0.0037\\ & 11& & 0.0222&0.0462&0.0845&0.1366&0.1559&0.1943&0.2402&0.2501&0.2056&0.1142&0.0259\\ & 12& & 0.0056&0.0141&0.0317&0.0634&0.0779&0.1134&0.1802&0.2501&0.2912&0.2570&0.1229\\ & 13& & 0.0009&0.0027&0.0073&0.0181&0.0240&0.0407&0.0832&0.1539&0.2539&0.3559&0.3593\\ & 14& & 0.0001&0.0002&0.0008&0.0024&0.0034&0.0068&0.0178&0.0440&0.1028&0.2288&0.4877\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 14& 0& & 0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0009&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0056&0.0019&0.0005&0.0001&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0222&0.0093&0.0033&0.0010&0.0006&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0611&0.0312&0.0136&0.0049&0.0033&0.0014&0.0003&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.1222&0.0762&0.0408&0.0183&0.0134&0.0066&0.0018&0.0003&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.1833&0.1398&0.0918&0.0510&0.0402&0.0232&0.0082&0.0020&0.0003&\phantom{0}&\phantom{0}\\ & 7& & 0.2095&0.1952&0.1574&0.1082&0.0918&0.0618&0.0280&0.0092&0.0019&0.0002&\phantom{0}\\ & 8& & 0.1833&0.2088&0.2066&0.1759&0.1607&0.1262&0.0734&0.0322&0.0093&0.0013&\phantom{0}\\ & 9& & 0.1222&0.1701&0.2066&0.2178&0.2143&0.1963&0.1468&0.0860&0.0352&0.0078&0.0004\\ & 10& & 0.0611&0.1040&0.1549&0.2022&0.2143&0.2290&0.2202&0.1720&0.0998&0.0349&0.0037\\ & 11& & 0.0222&0.0462&0.0845&0.1366&0.1559&0.1943&0.2402&0.2501&0.2056&0.1142&0.0259\\ & 12& & 0.0056&0.0141&0.0317&0.0634&0.0779&0.1134&0.1802&0.2501&0.2912&0.2570&0.1229\\ & 13& & 0.0009&0.0027&0.0073&0.0181&0.0240&0.0407&0.0832&0.1539&0.2539&0.3559&0.3593\\ & 14& & 0.0001&0.0002&0.0008&0.0024&0.0034&0.0068&0.0178&0.0440&0.1028&0.2288&0.4877\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
15& 0& & 0.8601&0.4633&0.2059&0.0874&0.0352&0.0134&0.0047&0.0023&0.0016&0.0005&0.0001\\
&1 & & 0.1303&0.3658&0.3432&0.2312&0.1319&0.0668&0.0305&0.0171&0.0126&0.0047&0.0016\\
& 2& & 0.0092&0.1348&0.2669&0.2856&0.2309&0.1559&0.0916&0.0599&0.0476&0.0219&0.0090\\
& 3& & 0.0004&0.0307&0.1285&0.2184&0.2501&0.2252&0.1700&0.1299&0.1110&0.0634&0.0318\\
& 4& & \phantom{0}&0.0049&0.0428&0.1156&0.1876&0.2252&0.2186&0.1948&0.1792&0.1268&0.0780\\
& 5& & \phantom{0}&0.0006&0.0105&0.0449&0.1032&0.1651&0.2061&0.2143&0.2123&0.1859&0.1404\\
& 6& & \phantom{0}&\phantom{0}&0.0019&0.0132&0.0430&0.0917&0.1472&0.1786&0.1906&0.2066&0.1914\\
& 7& & \phantom{0}&\phantom{0}&0.0003&0.0030&0.0138&0.0393&0.0811&0.1148&0.1319&0.1771&0.2013\\
& 8& & \phantom{0}&\phantom{0}&\phantom{0}&0.0005&0.0035&0.0131&0.0348&0.0574&0.0710&0.1181&0.1647\\
&9 & & \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0007&0.0034&0.0116&0.0223&0.0298&0.0612&0.1048\\
&10 & & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0007&0.0030&0.0067&0.0096&0.0245&0.0515\\
& 11& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0006&0.0015&0.0024&0.0074&0.0191\\
&12 & & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0004&0.0016&0.0052\\
& 13& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0010\\
& 14& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
& 15& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 15& 0& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0032&0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0139&0.0052&0.0016&0.0004&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0417&0.0191&0.0074&0.0024&0.0015&0.0006&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ &5 & & 0.0916&0.0515&0.0245&0.0096&0.0067&0.0030&0.0007&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.1527&0.1048&0.0612&0.0298&0.0223&0.0116&0.0034&0.0007&0.0001&\phantom{0}&\phantom{0}\\ & 7& & 0.1964&0.1647&0.1181&0.0710&0.0574&0.0348&0.0131&0.0035&0.0005&\phantom{0}&\phantom{0}\\ &8 & & 0.1964&0.2013&0.1771&0.1319&0.1148&0.0811&0.0393&0.0138&0.0030&0.0003&\phantom{0}\\ & 9& & 0.1527&0.1914&0.2066&0.1906&0.1786&0.1472&0.0917&0.0430&0.0132&0.0019&\phantom{0}\\ &10 & & 0.0916&0.1404&0.1859&0.2123&0.2143&0.2061&0.1651&0.1032&0.0449&0.0105&0.0006\\ & 11& & 0.0417&0.0780&0.1268&0.1792&0.1948&0.2186&0.2252&0.1876&0.1156&0.0428&0.0049\\ & 12& & 0.0139&0.0318&0.0634&0.1110&0.1299&0.1700&0.2252&0.2501&0.2184&0.1285&0.0307\\ &13 & & 0.0032&0.0090&0.0219&0.0476&0.0599&0.0916&0.1559&0.2309&0.2856&0.2669&0.1348\\ & 14& & 0.0005&0.0016&0.0047&0.0126&0.0171&0.0305&0.0668&0.1319&0.2312&0.3432&0.3658\\ & 15& & \phantom{0}&0.0001&0.0005&0.0016&0.0023&0.0047&0.0134&0.0352&0.0874&0.2059&0.4633\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 15& 0& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0032&0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0139&0.0052&0.0016&0.0004&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0417&0.0191&0.0074&0.0024&0.0015&0.0006&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ &5 & & 0.0916&0.0515&0.0245&0.0096&0.0067&0.0030&0.0007&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.1527&0.1048&0.0612&0.0298&0.0223&0.0116&0.0034&0.0007&0.0001&\phantom{0}&\phantom{0}\\ & 7& & 0.1964&0.1647&0.1181&0.0710&0.0574&0.0348&0.0131&0.0035&0.0005&\phantom{0}&\phantom{0}\\ &8 & & 0.1964&0.2013&0.1771&0.1319&0.1148&0.0811&0.0393&0.0138&0.0030&0.0003&\phantom{0}\\ & 9& & 0.1527&0.1914&0.2066&0.1906&0.1786&0.1472&0.0917&0.0430&0.0132&0.0019&\phantom{0}\\ &10 & & 0.0916&0.1404&0.1859&0.2123&0.2143&0.2061&0.1651&0.1032&0.0449&0.0105&0.0006\\ & 11& & 0.0417&0.0780&0.1268&0.1792&0.1948&0.2186&0.2252&0.1876&0.1156&0.0428&0.0049\\ & 12& & 0.0139&0.0318&0.0634&0.1110&0.1299&0.1700&0.2252&0.2501&0.2184&0.1285&0.0307\\ &13 & & 0.0032&0.0090&0.0219&0.0476&0.0599&0.0916&0.1559&0.2309&0.2856&0.2669&0.1348\\ & 14& & 0.0005&0.0016&0.0047&0.0126&0.0171&0.0305&0.0668&0.1319&0.2312&0.3432&0.3658\\ & 15& & \phantom{0}&0.0001&0.0005&0.0016&0.0023&0.0047&0.0134&0.0352&0.0874&0.2059&0.4633\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
16& 0& & 0.8515&0.4401&0.1853&0.0743&0.0281&0.0100&0.0033&0.0015&0.0010&0.0003&0.0001\\
&1 & & 0.1376&0.3706&0.3294&0.2097&0.1126&0.0535&0.0228&0.0122&0.0087&0.0030&0.0009\\
& 2& & 0.0104&0.1463&0.2745&0.2775&0.2111&0.1336&0.0732&0.0457&0.0353&0.0150&0.0056\\
& 3& & 0.0005&0.0359&0.1423&0.2285&0.2463&0.2079&0.1465&0.1066&0.0888&0.0468&0.0215\\
& 4& & \phantom{0}&0.0061&0.0514&0.1311&0.2001&0.2252&0.2040&0.1732&0.1553&0.1014&0.0572\\
&5 & & \phantom{0}&0.0008&0.0137&0.0555&0.1201&0.1802&0.2099&0.2078&0.2008&0.1623&0.1123\\
& 6& & \phantom{0}&0.0001&0.0028&0.0180&0.0550&0.1101&0.1649&0.1905&0.1982&0.1983&0.1684\\
& 7& & \phantom{0}&\phantom{0}&0.0004&0.0045&0.0197&0.0524&0.1010&0.1361&0.1524&0.1889&0.1969\\
& 8& & \phantom{0}&\phantom{0}&0.0001&0.0009&0.0055&0.0197&0.0487&0.0765&0.0923&0.1417&0.1812\\
& 9& & \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0012&0.0058&0.0185&0.0340&0.0442&0.0840&0.1318\\
& 10& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0014&0.0056&0.0119&0.0167&0.0392&0.0755\\
& 11& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0013&0.0032&0.0049&0.0142&0.0337\\
& 12& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0007&0.0011&0.0040&0.0115\\
& 13& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0008&0.0029\\
& 14& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0005\\
& 15& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
& 16& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 16& 0& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0018&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0085&0.0029&0.0008&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0278&0.0115&0.0040&0.0011&0.0007&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0667&0.0337&0.0142&0.0049&0.0032&0.0013&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.1222&0.0755&0.0392&0.0167&0.0119&0.0056&0.0014&0.0002&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.1746&0.1318&0.0840&0.0442&0.0340&0.0185&0.0058&0.0012&0.0001&\phantom{0}&\phantom{0}\\ & 8& & 0.1964&0.1812&0.1417&0.0923&0.0765&0.0487&0.0197&0.0055&0.0009&0.0001&\phantom{0}\\ & 9& & 0.1746&0.1969&0.1889&0.1524&0.1361&0.1010&0.0524&0.0197&0.0045&0.0004&\phantom{0}\\ & 10& & 0.1222&0.1684&0.1983&0.1982&0.1905&0.1649&0.1101&0.0550&0.0180&0.0028&0.0001\\ & 11& & 0.0667&0.1123&0.1623&0.2008&0.2078&0.2099&0.1802&0.1201&0.0555&0.0137&0.0008\\ & 12& & 0.0278&0.0572&0.1014&0.1553&0.1732&0.2040&0.2252&0.2001&0.1311&0.0514&0.0061\\ & 13& & 0.0085&0.0215&0.0468&0.0888&0.1066&0.1465&0.2079&0.2463&0.2285&0.1423&0.0359\\ & 14& & 0.0018&0.0056&0.0150&0.0353&0.0457&0.0732&0.1336&0.2111&0.2775&0.2745&0.1463\\ & 15& & 0.0002&0.0009&0.0030&0.0087&0.0122&0.0228&0.0535&0.1126&0.2097&0.3294&0.3706\\ & 16& & \phantom{0}&0.0001&0.0003&0.0010&0.0015&0.0033&0.0100&0.0281&0.0743&0.1853&0.4401\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 16& 0& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0018&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0085&0.0029&0.0008&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0278&0.0115&0.0040&0.0011&0.0007&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0667&0.0337&0.0142&0.0049&0.0032&0.0013&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.1222&0.0755&0.0392&0.0167&0.0119&0.0056&0.0014&0.0002&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.1746&0.1318&0.0840&0.0442&0.0340&0.0185&0.0058&0.0012&0.0001&\phantom{0}&\phantom{0}\\ & 8& & 0.1964&0.1812&0.1417&0.0923&0.0765&0.0487&0.0197&0.0055&0.0009&0.0001&\phantom{0}\\ & 9& & 0.1746&0.1969&0.1889&0.1524&0.1361&0.1010&0.0524&0.0197&0.0045&0.0004&\phantom{0}\\ & 10& & 0.1222&0.1684&0.1983&0.1982&0.1905&0.1649&0.1101&0.0550&0.0180&0.0028&0.0001\\ & 11& & 0.0667&0.1123&0.1623&0.2008&0.2078&0.2099&0.1802&0.1201&0.0555&0.0137&0.0008\\ & 12& & 0.0278&0.0572&0.1014&0.1553&0.1732&0.2040&0.2252&0.2001&0.1311&0.0514&0.0061\\ & 13& & 0.0085&0.0215&0.0468&0.0888&0.1066&0.1465&0.2079&0.2463&0.2285&0.1423&0.0359\\ & 14& & 0.0018&0.0056&0.0150&0.0353&0.0457&0.0732&0.1336&0.2111&0.2775&0.2745&0.1463\\ & 15& & 0.0002&0.0009&0.0030&0.0087&0.0122&0.0228&0.0535&0.1126&0.2097&0.3294&0.3706\\ & 16& & \phantom{0}&0.0001&0.0003&0.0010&0.0015&0.0033&0.0100&0.0281&0.0743&0.1853&0.4401\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
17& 0& &0.8429&0.4181&0.1668&0.0631&0.0225&0.0075&0.0023&0.0010&0.0007&0.0002&\phantom{0}\\
& 1& &0.1447&0.3741&0.3150&0.1893&0.0957&0.0426&0.0169&0.0086&0.0060&0.0019&0.0005\\
& 2& &0.0117&0.1575&0.2800&0.2673&0.1914&0.1136&0.0581&0.0345&0.0260&0.0102&0.0035\\
& 3& &0.0006&0.0415&0.1556&0.2359&0.2393&0.1893&0.1245&0.0863&0.0701&0.0341&0.0144\\
& 4& &\phantom{0}&0.0076&0.0605&0.1457&0.2093&0.2209&0.1868&0.1510&0.1320&0.0796&0.0411\\
& 5& &\phantom{0}&0.0010&0.0175&0.0668&0.1361&0.1914&0.2081&0.1963&0.1849&0.1379&0.0875\\
& 6& &\phantom{0}&0.0001&0.0039&0.0236&0.0680&0.1276&0.1784&0.1963&0.1991&0.1839&0.1432\\
& 7& &\phantom{0}&\phantom{0}&0.0007&0.0065&0.0267&0.0668&0.1201&0.1542&0.1685&0.1927&0.1841\\
& 8& &\phantom{0}&\phantom{0}&0.0001&0.0014&0.0084&0.0279&0.0644&0.0964&0.1134&0.1606&0.1883\\
& 9& &\phantom{0}&\phantom{0}&\phantom{0}&0.0003&0.0021&0.0093&0.0276&0.0482&0.0611&0.1070&0.1540\\
& 10& &\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0004&0.0025&0.0095&0.0193&0.0263&0.0571&0.1008\\
& 11& &\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0005&0.0026&0.0061&0.0090&0.0242&0.0525\\
& 12& &\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0006&0.0015&0.0024&0.0081&0.0215\\
& 13& &\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0005&0.0021&0.0068\\
& 14& &\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0004&0.0016\\
& 15& &\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003\\
& 16& &\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
& 17& &\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 17& 0& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0052&0.0016&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0182&0.0068&0.0021&0.0005&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0472&0.0215&0.0081&0.0024&0.0015&0.0006&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.0944&0.0525&0.0242&0.0090&0.0061&0.0026&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.1484&0.1008&0.0571&0.0263&0.0193&0.0095&0.0025&0.0004&\phantom{0}&\phantom{0}&\phantom{0}\\ & 8& & 0.1855&0.1540&0.1070&0.0611&0.0482&0.0276&0.0093&0.0021&0.0003&\phantom{0}&\phantom{0}\\ & 9& & 0.1855&0.1883&0.1606&0.1134&0.0964&0.0644&0.0279&0.0084&0.0014&0.0001&\phantom{0}\\ & 10& & 0.1484&0.1841&0.1927&0.1685&0.1542&0.1201&0.0668&0.0267&0.0065&0.0007&\phantom{0}\\ & 11& & 0.0944&0.1432&0.1839&0.1991&0.1963&0.1784&0.1276&0.0680&0.0236&0.0039&0.0001\\ & 12& & 0.0472&0.0875&0.1379&0.1849&0.1963&0.2081&0.1914&0.1361&0.0668&0.0175&0.0010\\ & 13& & 0.0182&0.0411&0.0796&0.1320&0.1510&0.1868&0.2209&0.2093&0.1457&0.0605&0.0076\\ & 14& & 0.0052&0.0144&0.0341&0.0701&0.0863&0.1245&0.1893&0.2393&0.2359&0.1556&0.0415\\ & 15& & 0.0010&0.0035&0.0102&0.0260&0.0345&0.0581&0.1136&0.1914&0.2673&0.2800&0.1575\\ & 16& & 0.0001&0.0005&0.0019&0.0060&0.0086&0.0169&0.0426&0.0957&0.1893&0.3150&0.3741\\ & 17& & \phantom{0}&\phantom{0}&0.0002&0.0007&0.0010&0.0023&0.0075&0.0225&0.0631&0.1668&0.4181\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 17& 0& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0010&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0052&0.0016&0.0004&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0182&0.0068&0.0021&0.0005&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0472&0.0215&0.0081&0.0024&0.0015&0.0006&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.0944&0.0525&0.0242&0.0090&0.0061&0.0026&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.1484&0.1008&0.0571&0.0263&0.0193&0.0095&0.0025&0.0004&\phantom{0}&\phantom{0}&\phantom{0}\\ & 8& & 0.1855&0.1540&0.1070&0.0611&0.0482&0.0276&0.0093&0.0021&0.0003&\phantom{0}&\phantom{0}\\ & 9& & 0.1855&0.1883&0.1606&0.1134&0.0964&0.0644&0.0279&0.0084&0.0014&0.0001&\phantom{0}\\ & 10& & 0.1484&0.1841&0.1927&0.1685&0.1542&0.1201&0.0668&0.0267&0.0065&0.0007&\phantom{0}\\ & 11& & 0.0944&0.1432&0.1839&0.1991&0.1963&0.1784&0.1276&0.0680&0.0236&0.0039&0.0001\\ & 12& & 0.0472&0.0875&0.1379&0.1849&0.1963&0.2081&0.1914&0.1361&0.0668&0.0175&0.0010\\ & 13& & 0.0182&0.0411&0.0796&0.1320&0.1510&0.1868&0.2209&0.2093&0.1457&0.0605&0.0076\\ & 14& & 0.0052&0.0144&0.0341&0.0701&0.0863&0.1245&0.1893&0.2393&0.2359&0.1556&0.0415\\ & 15& & 0.0010&0.0035&0.0102&0.0260&0.0345&0.0581&0.1136&0.1914&0.2673&0.2800&0.1575\\ & 16& & 0.0001&0.0005&0.0019&0.0060&0.0086&0.0169&0.0426&0.0957&0.1893&0.3150&0.3741\\ & 17& & \phantom{0}&\phantom{0}&0.0002&0.0007&0.0010&0.0023&0.0075&0.0225&0.0631&0.1668&0.4181\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
18& 0& & 0.8345&0.3972&0.1501&0.0536&0.0180&0.0056&0.0016&0.0007&0.0004&0.0001&\phantom{0}\\
& 1& & 0.1517&0.3763&0.3002&0.1704&0.0811&0.0338&0.0126&0.0061&0.0042&0.0012&0.0003\\
& 2& & 0.0130&0.1683&0.2835&0.2556&0.1723&0.0958&0.0458&0.0259&0.0190&0.0069&0.0022\\
& 3& & 0.0007&0.0473&0.1680&0.2406&0.2297&0.1704&0.1046&0.0690&0.0547&0.0246&0.0095\\
& 4& & \phantom{0}&0.0093&0.0700&0.1592&0.2153&0.2130&0.1681&0.1294&0.1104&0.0614&0.0291\\
& 5& & \phantom{0}&0.0014&0.0218&0.0787&0.1507&0.1988&0.2017&0.1812&0.1664&0.1146&0.0666\\
& 6& & \phantom{0}&0.0002&0.0052&0.0301&0.0816&0.1436&0.1873&0.1963&0.1941&0.1655&0.1181\\
&7 & & \phantom{0}&\phantom{0}&0.0010&0.0091&0.0350&0.0820&0.1376&0.1682&0.1792&0.1892&0.1657\\
& 8& & \phantom{0}&\phantom{0}&0.0002&0.0022&0.0120&0.0376&0.0811&0.1157&0.1327&0.1734&0.1864\\
& 9& & \phantom{0}&\phantom{0}&\phantom{0}&0.0004&0.0033&0.0139&0.0386&0.0643&0.0794&0.1284&0.1694\\
& 10& & \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0008&0.0042&0.0149&0.0289&0.0385&0.0771&0.1248\\
& 11& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0010&0.0046&0.0105&0.0151&0.0374&0.0742\\
& 12& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0012&0.0031&0.0047&0.0145&0.0354\\
& 13& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0007&0.0012&0.0045&0.0134\\
& 14& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0002&0.0011&0.0039\\
& 15& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0009\\
& 16& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
& 17& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
& 18& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 18&0 & & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0006&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0031&0.0009&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0117&0.0039&0.0011&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0327&0.0134&0.0045&0.0012&0.0007&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.0708&0.0354&0.0145&0.0047&0.0031&0.0012&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.1214&0.0742&0.0374&0.0151&0.0105&0.0046&0.0010&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 8& & 0.1669&0.1248&0.0771&0.0385&0.0289&0.0149&0.0042&0.0008&0.0001&\phantom{0}&\phantom{0}\\ & 9& & 0.1855&0.1694&0.1284&0.0794&0.0643&0.0386&0.0139&0.0033&0.0004&\phantom{0}&\phantom{0}\\ & 10& & 0.1669&0.1864&0.1734&0.1327&0.1157&0.0811&0.0376&0.0120&0.0022&0.0002&\phantom{0}\\ & 11& & 0.1214&0.1657&0.1892&0.1792&0.1682&0.1376&0.0820&0.0350&0.0091&0.0010&\phantom{0}\\ & 12& & 0.0708&0.1181&0.1655&0.1941&0.1963&0.1873&0.1436&0.0816&0.0301&0.0052&0.0002\\ & 13& & 0.0327&0.0666&0.1146&0.1664&0.1812&0.2017&0.1988&0.1507&0.0787&0.0218&0.0014\\ & 14& & 0.0117&0.0291&0.0614&0.1104&0.1294&0.1681&0.2130&0.2153&0.1592&0.0700&0.0093\\ & 15& & 0.0031&0.0095&0.0246&0.0547&0.0690&0.1046&0.1704&0.2297&0.2406&0.1680&0.0473\\ & 16& & 0.0006&0.0022&0.0069&0.0190&0.0259&0.0458&0.0958&0.1723&0.2556&0.2835&0.1683\\ & 17& & 0.0001&0.0003&0.0012&0.0042&0.0061&0.0126&0.0338&0.0811&0.1704&0.3002&0.3763\\ & 18& & \phantom{0}&\phantom{0}&0.0001&0.0004&0.0007&0.0016&0.0056&0.0180&0.0536&0.1501&0.3972\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 18&0 & & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & 0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0006&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0031&0.0009&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0117&0.0039&0.0011&0.0002&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0327&0.0134&0.0045&0.0012&0.0007&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.0708&0.0354&0.0145&0.0047&0.0031&0.0012&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.1214&0.0742&0.0374&0.0151&0.0105&0.0046&0.0010&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 8& & 0.1669&0.1248&0.0771&0.0385&0.0289&0.0149&0.0042&0.0008&0.0001&\phantom{0}&\phantom{0}\\ & 9& & 0.1855&0.1694&0.1284&0.0794&0.0643&0.0386&0.0139&0.0033&0.0004&\phantom{0}&\phantom{0}\\ & 10& & 0.1669&0.1864&0.1734&0.1327&0.1157&0.0811&0.0376&0.0120&0.0022&0.0002&\phantom{0}\\ & 11& & 0.1214&0.1657&0.1892&0.1792&0.1682&0.1376&0.0820&0.0350&0.0091&0.0010&\phantom{0}\\ & 12& & 0.0708&0.1181&0.1655&0.1941&0.1963&0.1873&0.1436&0.0816&0.0301&0.0052&0.0002\\ & 13& & 0.0327&0.0666&0.1146&0.1664&0.1812&0.2017&0.1988&0.1507&0.0787&0.0218&0.0014\\ & 14& & 0.0117&0.0291&0.0614&0.1104&0.1294&0.1681&0.2130&0.2153&0.1592&0.0700&0.0093\\ & 15& & 0.0031&0.0095&0.0246&0.0547&0.0690&0.1046&0.1704&0.2297&0.2406&0.1680&0.0473\\ & 16& & 0.0006&0.0022&0.0069&0.0190&0.0259&0.0458&0.0958&0.1723&0.2556&0.2835&0.1683\\ & 17& & 0.0001&0.0003&0.0012&0.0042&0.0061&0.0126&0.0338&0.0811&0.1704&0.3002&0.3763\\ & 18& & \phantom{0}&\phantom{0}&0.0001&0.0004&0.0007&0.0016&0.0056&0.0180&0.0536&0.1501&0.3972\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
19& 0& & 0.8262&0.3774&0.1351&0.0456&0.0144&0.0042&0.0011&0.0005&0.0003&0.0001&\phantom{0}\\
& 1& & 0.1586&0.3774&0.2852&0.1529&0.0685&0.0268&0.0093&0.0043&0.0029&0.0008&0.0002\\
& 2& & 0.0144&0.1787&0.2852&0.2428&0.1540&0.0803&0.0358&0.0193&0.0138&0.0046&0.0013\\
& 3& & 0.0008&0.0533&0.1796&0.2428&0.2182&0.1517&0.0869&0.0546&0.0422&0.0175&0.0062\\
& 4& & \phantom{0}&0.0112&0.0798&0.1714&0.2182&0.2023&0.1491&0.1093&0.0909&0.0467&0.0203\\
& 5& & \phantom{0}&0.0018&0.0266&0.0907&0.1636&0.2023&0.1916&0.1639&0.1468&0.0933&0.0497\\
& 6& & \phantom{0}&0.0002&0.0069&0.0374&0.0955&0.1574&0.1916&0.1912&0.1844&0.1451&0.0949\\
& 7& & \phantom{0}&\phantom{0}&0.0014&0.0122&0.0443&0.0974&0.1525&0.1776&0.1844&0.1797&0.1443\\
& 8& & \phantom{0}&\phantom{0}&0.0002&0.0032&0.0166&0.0487&0.0981&0.1332&0.1489&0.1797&0.1771\\
& 9& & \phantom{0}&\phantom{0}&\phantom{0}&0.0007&0.0051&0.0198&0.0514&0.0814&0.0980&0.1464&0.1771\\
& 10& & \phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0013&0.0066&0.0220&0.0407&0.0528&0.0976&0.1449\\
& 11& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0003&0.0018&0.0077&0.0166&0.0233&0.0532&0.0970\\
& 12& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0004&0.0022&0.0055&0.0083&0.0237&0.0529\\
& 13& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0005&0.0015&0.0024&0.0085&0.0233\\
& 14& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0006&0.0024&0.0082\\
& 15& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0001&0.0005&0.0022\\
& 16& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0005\\
& 17& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001\\
& 18& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
& 19& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 19& 0& & \phantom{0}1&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0018&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0074&0.0022&0.0005&0.0001&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0222&0.0082&0.0024&0.0006&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.0518&0.0233&0.0085&0.0024&0.0015&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.0961&0.0529&0.0237&0.0083&0.0055&0.0022&0.0004&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 8& & 0.1442&0.0970&0.0532&0.0233&0.0166&0.0077&0.0018&0.0003&\phantom{0}&\phantom{0}&\phantom{0}\\ & 9& & 0.1762&0.1449&0.0976&0.0528&0.0407&0.0220&0.0066&0.0013&0.0001&\phantom{0}&\phantom{0}\\ & 10& & 0.1762&0.1771&0.1464&0.0980&0.0814&0.0514&0.0198&0.0051&0.0007&\phantom{0}&\phantom{0}\\ & 11& & 0.1442&0.1771&0.1797&0.1489&0.1332&0.0981&0.0487&0.0166&0.0032&0.0002&\phantom{0}\\ & 12& & 0.0961&0.1443&0.1797&0.1844&0.1776&0.1525&0.0974&0.0443&0.0122&0.0014&\phantom{0}\\ & 13& & 0.0518&0.0949&0.1451&0.1844&0.1912&0.1916&0.1574&0.0955&0.0374&0.0069&0.0002\\ & 14& & 0.0222&0.0497&0.0933&0.1468&0.1639&0.1916&0.2023&0.1636&0.0907&0.0266&0.0018\\ & 15& & 0.0074&0.0203&0.0467&0.0909&0.1093&0.1491&0.2023&0.2182&0.1714&0.0798&0.0112\\ & 16& & 0.0018&0.0062&0.0175&0.0422&0.0546&0.0869&0.1517&0.2182&0.2428&0.1796&0.0533\\ & 17& & 0.0003&0.0013&0.0046&0.0138&0.0193&0.0358&0.0803&0.1540&0.2428&0.2852&0.1787\\ & 18& & \phantom{0}&0.0002&0.0008&0.0029&0.0043&0.0093&0.0268&0.0685&0.1529&0.2852&0.3774\\ & 19& & \phantom{0}&\phantom{0}&0.0001&0.0003&0.0005&0.0011&0.0042&0.0144&0.0456&0.1351&0.3774\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 19& 0& & \phantom{0}1&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0018&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0074&0.0022&0.0005&0.0001&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0222&0.0082&0.0024&0.0006&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.0518&0.0233&0.0085&0.0024&0.0015&0.0005&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.0961&0.0529&0.0237&0.0083&0.0055&0.0022&0.0004&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 8& & 0.1442&0.0970&0.0532&0.0233&0.0166&0.0077&0.0018&0.0003&\phantom{0}&\phantom{0}&\phantom{0}\\ & 9& & 0.1762&0.1449&0.0976&0.0528&0.0407&0.0220&0.0066&0.0013&0.0001&\phantom{0}&\phantom{0}\\ & 10& & 0.1762&0.1771&0.1464&0.0980&0.0814&0.0514&0.0198&0.0051&0.0007&\phantom{0}&\phantom{0}\\ & 11& & 0.1442&0.1771&0.1797&0.1489&0.1332&0.0981&0.0487&0.0166&0.0032&0.0002&\phantom{0}\\ & 12& & 0.0961&0.1443&0.1797&0.1844&0.1776&0.1525&0.0974&0.0443&0.0122&0.0014&\phantom{0}\\ & 13& & 0.0518&0.0949&0.1451&0.1844&0.1912&0.1916&0.1574&0.0955&0.0374&0.0069&0.0002\\ & 14& & 0.0222&0.0497&0.0933&0.1468&0.1639&0.1916&0.2023&0.1636&0.0907&0.0266&0.0018\\ & 15& & 0.0074&0.0203&0.0467&0.0909&0.1093&0.1491&0.2023&0.2182&0.1714&0.0798&0.0112\\ & 16& & 0.0018&0.0062&0.0175&0.0422&0.0546&0.0869&0.1517&0.2182&0.2428&0.1796&0.0533\\ & 17& & 0.0003&0.0013&0.0046&0.0138&0.0193&0.0358&0.0803&0.1540&0.2428&0.2852&0.1787\\ & 18& & \phantom{0}&0.0002&0.0008&0.0029&0.0043&0.0093&0.0268&0.0685&0.1529&0.2852&0.3774\\ & 19& & \phantom{0}&\phantom{0}&0.0001&0.0003&0.0005&0.0011&0.0042&0.0144&0.0456&0.1351&0.3774\\ \hline \end{array} $$
$$
\begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\hline
n \downarrow & X \downarrow & p \to & 0.01 & 0.05 & 0.10& 0.15 & 0.20 & 0.25 & 0.30 & 1/3 & 0.35 & 0.40 & 0.45 \\
\hline
20& 0& & 0.8179&0.3585&0.1216&0.0388&0.0115&0.0032&0.0008&0.0003&0.0002&\phantom{0}&\phantom{0}\\
& 1& & 0.1652&0.3774&0.2702&0.1368&0.0576&0.0211&0.0068&0.0030&0.0020&0.0005&0.0001\\
& 2& & 0.0159&0.1887&0.2852&0.2293&0.1369&0.0669&0.0278&0.0143&0.0100&0.0031&0.0008\\
& 3& & 0.0010&0.0596&0.1901&0.2428&0.2054&0.1339&0.0716&0.0429&0.0323&0.0123&0.0040\\
& 4& & \phantom{0}&0.0133&0.0898&0.1821&0.2182&0.1897&0.1304&0.0911&0.0738&0.0350&0.0139\\
& 5& & \phantom{0}&0.0022&0.0319&0.1028&0.1746&0.2023&0.1789&0.1457&0.1272&0.0746&0.0365\\
& 6& & \phantom{0}&0.0003&0.0089&0.0454&0.1091&0.1686&0.1916&0.1821&0.1712&0.1244&0.0746\\
& 7& & \phantom{0}&\phantom{0}&0.0020&0.0160&0.0545&0.1124&0.1643&0.1821&0.1844&0.1659&0.1221\\
& 8& & \phantom{0}&\phantom{0}&0.0004&0.0046&0.0222&0.0609&0.1144&0.1480&0.1614&0.1797&0.1623\\
& 9& & \phantom{0}&\phantom{0}&0.0001&0.0011&0.0074&0.0271&0.0654&0.0987&0.1158&0.1597&0.1771\\
& 10& & \phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0020&0.0099&0.0308&0.0543&0.0686&0.1171&0.1593\\
& 11& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0005&0.0030&0.0120&0.0247&0.0336&0.0710&0.1185\\
& 12& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0008&0.0039&0.0092&0.0136&0.0355&0.0727\\
&13 & & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0010&0.0028&0.0045&0.0146&0.0366\\
& 14& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0007&0.0012&0.0049&0.0150\\
& 15& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0001&0.0003&0.0013&0.0049\\
& 16& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0003&0.0013\\
& 17& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&0.0002\\
& 18& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
& 19& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
& 20& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\
\hline
\end{array}
$$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 20& 0& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0011&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0046&0.0013&0.0003&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0148&0.0049&0.0013&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.0370&0.0150&0.0049&0.0012&0.0007&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.0739&0.0366&0.0146&0.0045&0.0028&0.0010&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 8& & 0.1201&0.0727&0.0355&0.0136&0.0092&0.0039&0.0008&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 9& & 0.1602&0.1185&0.0710&0.0336&0.0247&0.0120&0.0030&0.0005&\phantom{0}&\phantom{0}&\phantom{0}\\ & 10& & 0.1762&0.1593&0.1171&0.0686&0.0543&0.0308&0.0099&0.0020&0.0002&\phantom{0}&\phantom{0}\\ & 11& & 0.1602&0.1771&0.1597&0.1158&0.0987&0.0654&0.0271&0.0074&0.0011&0.0001&\phantom{0}\\ & 12& & 0.1201&0.1623&0.1797&0.1614&0.1480&0.1144&0.0609&0.0222&0.0046&0.0004&\phantom{0}\\ & 13& & 0.0739&0.1221&0.1659&0.1844&0.1821&0.1643&0.1124&0.0545&0.0160&0.0020&\phantom{0}\\ & 14& & 0.0370&0.0746&0.1244&0.1712&0.1821&0.1916&0.1686&0.1091&0.0454&0.0089&0.0003\\ & 15& & 0.0148&0.0365&0.0746&0.1272&0.1457&0.1789&0.2023&0.1746&0.1028&0.0319&0.0022\\ &16& & 0.0046&0.0139&0.0350&0.0738&0.0911&0.1304&0.1897&0.2182&0.1821&0.0898&0.0133\\ & 17& & 0.0011&0.0040&0.0123&0.0323&0.0429&0.0716&0.1339&0.2054&0.2428&0.1901&0.0596\\ & 18& & 0.0002&0.0008&0.0031&0.0100&0.0143&0.0278&0.0669&0.1369&0.2293&0.2852&0.1887\\ & 19& & \phantom{0}&0.0001&0.0005&0.0020&0.0030&0.0068&0.0211&0.0576&0.1368&0.2702&0.3774\\ & 20& & \phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0003&0.0008&0.0032&0.0115&0.0388&0.1216&0.3585\\ \hline \end{array} $$
$$ \begin{array}{r|r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r} \hline n \downarrow & X \downarrow & p \to & 0.50& 0.55 & 0.60 & 0.65& 2/3 & 0.70 & 0.75 & 0.80 & 0.85 & 0.90 & 0.95\\ \hline 20& 0& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 1& & \phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 2& & 0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 3& & 0.0011&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 4& & 0.0046&0.0013&0.0003&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 5& & 0.0148&0.0049&0.0013&0.0003&0.0001&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 6& & 0.0370&0.0150&0.0049&0.0012&0.0007&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 7& & 0.0739&0.0366&0.0146&0.0045&0.0028&0.0010&0.0002&\phantom{0}&\phantom{0}&\phantom{0}&\phantom{0}\\ & 8& & 0.1201&0.0727&0.0355&0.0136&0.0092&0.0039&0.0008&0.0001&\phantom{0}&\phantom{0}&\phantom{0}\\ & 9& & 0.1602&0.1185&0.0710&0.0336&0.0247&0.0120&0.0030&0.0005&\phantom{0}&\phantom{0}&\phantom{0}\\ & 10& & 0.1762&0.1593&0.1171&0.0686&0.0543&0.0308&0.0099&0.0020&0.0002&\phantom{0}&\phantom{0}\\ & 11& & 0.1602&0.1771&0.1597&0.1158&0.0987&0.0654&0.0271&0.0074&0.0011&0.0001&\phantom{0}\\ & 12& & 0.1201&0.1623&0.1797&0.1614&0.1480&0.1144&0.0609&0.0222&0.0046&0.0004&\phantom{0}\\ & 13& & 0.0739&0.1221&0.1659&0.1844&0.1821&0.1643&0.1124&0.0545&0.0160&0.0020&\phantom{0}\\ & 14& & 0.0370&0.0746&0.1244&0.1712&0.1821&0.1916&0.1686&0.1091&0.0454&0.0089&0.0003\\ & 15& & 0.0148&0.0365&0.0746&0.1272&0.1457&0.1789&0.2023&0.1746&0.1028&0.0319&0.0022\\ &16& & 0.0046&0.0139&0.0350&0.0738&0.0911&0.1304&0.1897&0.2182&0.1821&0.0898&0.0133\\ & 17& & 0.0011&0.0040&0.0123&0.0323&0.0429&0.0716&0.1339&0.2054&0.2428&0.1901&0.0596\\ & 18& & 0.0002&0.0008&0.0031&0.0100&0.0143&0.0278&0.0669&0.1369&0.2293&0.2852&0.1887\\ & 19& & \phantom{0}&0.0001&0.0005&0.0020&0.0030&0.0068&0.0211&0.0576&0.1368&0.2702&0.3774\\ & 20& & \phantom{0}&\phantom{0}&\phantom{0}&0.0002&0.0003&0.0008&0.0032&0.0115&0.0388&0.1216&0.3585\\ \hline \end{array} $$
