### Normal Distribution

The normal distribution is by far the most commonly occurring distribution. If you have no good reason for suspecting that your data is not normally distributed, do not use another distribution. The normal distribution class has two parameters, and which specify the location and scaling of the distribution.

- The value is the average or mean value.

- The value is the standard deviation, which is a measure of variability.

If X1, X2, . . . Xn is the set of sample measurement values, normal distribution parameters are calculated using the following formulae:

Mean:

Sigma:

The density function for the normal distribution is given by:

The normal distribution function cannot be expressed as a combination of common functions. The distribution function is given by:

For the special case where and , the distribution function is called the standard normal distribution and is denoted . That is: