The normal distribution is a 2-parameter distribution and covers any specified average and standard deviation. It is represented by a single point with a skewness of zero and kurtosis of three (excess kurtosis of zero) on a skewness-kurtosis plot as shown below:
The density function of the normal distribution is shown below:
The equation, parameters and bounds of the density function are:
The moments of the normal distribution can be calculated from the parameters as shown below:
The normal distribution is the distribution of addition and subtraction. The central limit theorem states that as items are added and subtracted together, under certain restrictions, the result will tend to the normal distribution. To see the central limit theory in practice, go to the Dice Experiments dialog box and specify 4 dice be added together as shown below.
The normal distribution fits the resulting data as shown below.