Normal Distribution

It’s a bell curve.

Density function: $f(x)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-\frac{1}{2}[\frac{x-\mu }{\sigma }{]}^2}$

P(x<a) is determined from a table of probabilities. Note that the $\frac{x-\mu }{\sigma }$ above is the same as z-score.

“Standard normal distribution” is a special case of the above formula, where $\mu =0,\sigma =1$

Seems most of the math for determining area under the curve takes into account that the full area under the curve = 1 and the items are symmetrical. From there, we can do simple logic to work out the area’s value b/c we can find the space from 0 to z using the tables.