The Normal Probability Distribution

Definition: If a continuous random variable has a probability distribution with a graph that is symmetric and bell-shaped, and it can be described by the function equation \[ f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2} \quad\quad -\infty \leq x \leq \infty\] then we say it has a normal distribution.

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Facts are stubborn things but statistics are pliable.

— Mark Twain