The Standard Normal Cumulative Distribution Function
(i.e., The $z$ Table)
Table Values Represent AREA to the LEFT of the Z score.
$$
\begin{array}{r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
z&0.00&0.01&0.02&0.03&0.04&0.05&0.06&0.07&0.08&0.09\\ \hline
\ \\
-3.5^{-}& 0.0001 &0.0001& 0.0001& 0.0001& 0.0001 &0.0001& 0.0001& 0.0001& 0.0001& 0.0001\\
-3.4 &0.0003& 0.0003& 0.0003& 0.0003 &0.0003 &0.0003& 0.0003& 0.0003& 0.0003& 0.0002\\
-3.3& 0.0005& 0.0005& 0.0005& 0.0004& 0.0004& 0.0004& 0.0004 &0.0004& 0.0004 &0.0003\\
-3.2 &0.0007& 0.0007& 0.0006 &0.0006& 0.0006& 0.0006& 0.0006& 0.0005 &0.0005& 0.0005\\
-3.1& 0.0010 &0.0009& 0.0009& 0.0009& 0.0008& 0.0008& 0.0008& 0.0008 &0.0007& 0.0007\\
-3.0& 0.0013& 0.0013& 0.0013 &0.0012& 0.0012& 0.0011& 0.0011& 0.0011 &0.0010& 0.0010\\
-2.9 &0.0019 &0.0018& 0.0018& 0.0017& 0.0016& 0.0016& 0.0015& 0.0015& 0.0014& 0.0014\\
-2.8& 0.0026 &0.0025& 0.0024& 0.0023& 0.0023& 0.0022& 0.0021& 0.0021& 0.0020& 0.0019\\
-2.7& 0.0035& 0.0034 &0.0033 &0.0032& 0.0031& 0.0030& 0.0029& 0.0028& 0.0027& 0.0026\\
-2.6& 0.0047 &0.0045& 0.0044 &0.0043& 0.0041 &0.0040 &0.0039 &0.0038& 0.0037& 0.0036\\
-2.5 &0.0062& 0.0060& 0.0059& 0.0057& 0.0055& 0.0054& 0.0052& 0.0051& 0.0049& 0.0048\\
-2.4 &0.0082& 0.0080& 0.0078& 0.0075& 0.0073& 0.0071 &0.0069 &0.0068& 0.0066& 0.0064\\
-2.3& 0.0107& 0.0104& 0.0102 &0.0099 &0.0096& 0.0094& 0.0091 &0.0089& 0.0087& 0.0084\\
-2.2& 0.0139 &0.0136& 0.0132& 0.0129& 0.0125& 0.0122& 0.0119& 0.0116& 0.0113& 0.0110\\
-2.1& 0.0179& 0.0174& 0.0170& 0.0166 &0.0162& 0.0158& 0.0154 &0.0150& 0.0146 &0.0143\\
-2.0 &0.0228 &0.0222& 0.0217& 0.0212& 0.0207& 0.0202& 0.0197 &0.0192& 0.0188 &0.0183\\
-1.9& 0.0287& 0.0281 &0.0274 &0.0268& 0.0262 &0.0256 &0.0250& 0.0244& 0.0239 &0.0233\\
-1.8 &0.0359 &0.0351& 0.0344& 0.0336& 0.0329 &0.0322& 0.0314 &0.0307& 0.0301 &0.0294\\
-1.7& 0.0446 &0.0436 &0.0427& 0.0418& 0.0409& 0.0401& 0.0392 &0.0384& 0.0375& 0.0367\\
-1.6& 0.0548 &0.0537& 0.0526& 0.0516& 0.0505& 0.0495& 0.0485& 0.0475& 0.0465& 0.0455\\
-1.5 &0.0668& 0.0655 &0.0643& 0.0630 &0.0618& 0.0606& 0.0594& 0.0582& 0.0571& 0.0559\\
-1.4& 0.0808& 0.0793& 0.0778& 0.0764& 0.0749& 0.0735& 0.0721& 0.0708 &0.0694 &0.0681\\
-1.3& 0.0968& 0.0951& 0.0934& 0.0918& 0.0901& 0.0885& 0.0869& 0.0853 &0.0838& 0.0823\\
-1.2 &0.1151& 0.1131& 0.1112 &0.1093 &0.1075& 0.1056 &0.1038 &0.1020& 0.1003& 0.0985\\
-1.1& 0.1357& 0.1335& 0.1314& 0.1292 &0.1271& 0.1251& 0.1230& 0.1210& 0.1190& 0.1170\\
-1.0 &0.1587& 0.1562& 0.1539& 0.1515& 0.1492& 0.1469 &0.1446& 0.1423& 0.1401& 0.1379\\
-0.9& 0.1841& 0.1814 &0.1788 &0.1762& 0.1736& 0.1711 &0.1685& 0.1660 &0.1635& 0.1611\\
-0.8 &0.2119& 0.2090 &0.2061 &0.2033& 0.2005 &0.1977& 0.1949& 0.1922& 0.1894 &0.1867\\
-0.7 &0.2420& 0.2389& 0.2358& 0.2327& 0.2296& 0.2266& 0.2236& 0.2206& 0.2177& 0.2148\\
-0.6& 0.2743 &0.2709& 0.2676& 0.2643 &0.2611 &0.2578& 0.2546& 0.2514& 0.2483& 0.2451\\
-0.5& 0.3085 &0.3050 &0.3015& 0.2981& 0.2946& 0.2912& 0.2877 &0.2843 &0.2810& 0.2776\\
-0.4& 0.3446 &0.3409 &0.3372 &0.3336 &0.3300 &0.3264& 0.3228& 0.3192 &0.3156& 0.3121\\
-0.3& 0.3821& 0.3783& 0.3745& 0.3707& 0.3669& 0.3632& 0.3594& 0.3557& 0.3520& 0.3483\\
-0.2& 0.4207 &0.4168& 0.4129& 0.4090& 0.4052& 0.4013 &0.3974 &0.3936& 0.3897& 0.3859\\
-0.1& 0.4602 &0.4562& 0.4522 &0.4483 &0.4443& 0.4404& 0.4364 &0.4325& 0.4286& 0.4247\\
0.0& 0.5000 &0.4960 &0.4920& 0.4880& 0.4840& 0.4801& 0.4761& 0.4721& 0.4681 &0.4641\\
\end{array}
$$
Table Values Represent AREA to the LEFT of the Z score.
$$
\begin{array}{r|r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
z&0.00&0.01&0.02&0.03&0.04&0.05&0.06&0.07&0.08&0.09\\ \hline
\ \\
0.0&0.5000&0.5040&0.5080&0.5120&0.5160&0.5199&0.5239&0.5279&0.5319&0.5359\\
0.1&0.5398&0.5438&0.5478&0.5517&0.5557&0.5596&0.5636&0.5675&0.5714&0.5753\\
0.2&0.5793&0.5832&0.5871&0.5910&0.5948&0.5987&0.6026&0.6064&0.6103&0.6141\\
0.3&0.6179&0.6217&0.6255&0.6293&0.6331&0.6368&0.6406&0.6443&0.6480&0.6517\\
0.4&0.6554&0.6591&0.6628&0.6664&0.6700&0.6736&0.6772&0.6808&0.6844&0.6879\\
0.5&0.6915&0.6950&0.6985&0.7019&0.7054&0.7088&0.7123&0.7157&0.7190&0.7224\\
0.6&0.7257&0.7291&0.7324&0.7357&0.7389&0.7422&0.7454&0.7486&0.7517&0.7549\\
0.7&0.7580&0.7611&0.7642&0.7673&0.7703&0.7734&0.7764&0.7794&0.7823&0.7852\\
0.8&0.7881&0.7910&0.7939&0.7967&0.7995&0.8023&0.8051&0.8078&0.8106&0.8133\\
0.9&0.8159&0.8186&0.8212&0.8238&0.8264&0.8289&0.8315&0.8340&0.8365&0.8389\\
1.0&0.8413&0.8438&0.8461&0.8485&0.8508&0.8531&0.8554&0.8577&0.8599&0.8621\\
1.1&0.8643&0.8665&0.8686&0.8708&0.8729&0.8749&0.8770&0.8790&0.8810&0.8830\\
1.2&0.8849&0.8869&0.8888&0.8907&0.8925&0.8944&0.8962&0.8980&0.8997&0.9015\\
1.3&0.9032&0.9049&0.9066&0.9082&0.9099&0.9115&0.9131&0.9147&0.9162&0.9177\\
1.4&0.9192&0.9207&0.9222&0.9236&0.9251&0.9265&0.9279&0.9292&0.9306&0.9319\\
1.5&0.9332&0.9345&0.9357&0.9370&0.9382&0.9394&0.9406&0.9418&0.9429&0.9441\\
1.6&0.9452&0.9463&0.9474&0.9484&0.9495&0.9505&0.9515&0.9525&0.9535&0.9545\\
1.7&0.9554&0.9564&0.9573&0.9582&0.9591&0.9599&0.9608&0.9616&0.9625&0.9633\\
1.8&0.9641&0.9649&0.9656&0.9664&0.9671&0.9678&0.9686&0.9693&0.9699&0.9706\\
1.9&0.9713&0.9719&0.9726&0.9732&0.9738&0.9744&0.9750&0.9756&0.9761&0.9767\\
2.0&0.9772&0.9778&0.9783&0.9788&0.9793&0.9798&0.9803&0.9808&0.9812&0.9817\\
2.1&0.9821&0.9826&0.9830&0.9834&0.9838&0.9842&0.9846&0.9850&0.9854&0.9857\\
2.2&0.9861&0.9864&0.9868&0.9871&0.9875&0.9878&0.9881&0.9884&0.9887&0.9890\\
2.3&0.9893&0.9896&0.9898&0.9901&0.9904&0.9906&0.9909&0.9911&0.9913&0.9916\\
2.4&0.9918&0.9920&0.9922&0.9925&0.9927&0.9929&0.9931&0.9932&0.9934&0.9936\\
2.5&0.9938&0.9940&0.9941&0.9943&0.9945&0.9946&0.9948&0.9949&0.9951&0.9952\\
2.6&0.9953&0.9955&0.9956&0.9957&0.9959&0.9960&0.9961&0.9962&0.9963&0.9964\\
2.7&0.9965&0.9966&0.9967&0.9968&0.9969&0.9970&0.9971&0.9972&0.9973&0.9974\\
2.8&0.9974&0.9975&0.9976&0.9977&0.9977&0.9978&0.9979&0.9979&0.9980&0.9981\\
2.9&0.9981&0.9982&0.9982&0.9983&0.9984&0.9984&0.9985&0.9985&0.9986&0.9986\\
3.0&0.9987&0.9987&0.9987&0.9988&0.9988&0.9989&0.9989&0.9989&0.9990&0.9990\\
3.1&0.9990&0.9991&0.9991&0.9991&0.9992&0.9992&0.9992&0.9992&0.9993&0.9993\\
3.2&0.9993&0.9993&0.9994&0.9994&0.9994&0.9994&0.9994&0.9995&0.9995&0.9995\\
3.3&0.9995&0.9995&0.9995&0.9996&0.9996&0.9996&0.9996&0.9996&0.9996&0.9997\\
3.4&0.9997&0.9997&0.9997&0.9997&0.9997&0.9997&0.9997&0.9997&0.9997&0.9998\\
3.5&0.9998&0.9998&0.9998&0.9998&0.9998&0.9998&0.9998&0.9998&0.9998&0.9998\\
3.6&0.9998&0.9998&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999\\
3.7&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999\\
3.8&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999&0.9999\\
3.9&1.0000&1.0000&1.0000&1.0000&1.0000&1.0000&1.0000&1.0000&1.0000&1.0000\\
\end{array}
$$
TI-83/84:
- To find the area between two z scores, press 2nd, VARS, 2 (for normalcdf), then proceed to enter the two z scores separated by a comma, as in (left z score, right z score).
- To find a z score corresponding to a known probability, press 2nd, VARS, 3 (for invNorm), and proceed to enter the total area to the left of the value, the mean, and the standard deviation in the format of (total area to the left, mean, standard devi-ation) with the commas included.
