Normal distribution/Definition

a symmetrical bell-shaped probability distribution having the probability function

$f(x;\mu ,\sigma )={\frac {1}{\sigma {\sqrt {2\pi }}}}\,e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}},$ where $\scriptstyle {\sigma }\$ is the standard deviation, and, $\scriptstyle {\mu }\$ is the expected value