# Statistics/Distributions/Normal

The Normal Probability Distribution is one of the most useful and more important distributions in statistics. It is a continuous variable distribution. Although the mathematics of this distribution can be quite off putting for students of a first course in statistics it can nevertheless be usefully applied with out over complication.

The Normal distribution is used frequently in statistics for many reasons:

1) The Normal distribution has many convenient mathematical properties.

2) Many natural phenomena have distributions which when studied have been shown to be close to that of the Normal Distribution.

3) The Central Limit Theorem shows that the Normal Distribution is a suitable model for large samples regardless of the actual distribution.

## Mathematical Characteristics of the Normal Distribution

A continuous random variable, X, is normally distributed with a probability density function:

${\displaystyle {\frac {1}{\sigma {\sqrt {2\pi }}}}\;\exp \left(-{\frac {\left(x-\mu \right)^{2}}{2\sigma ^{2}}}\right)\!}$