Computing Normal Probabilities
The normal distribution is the backbone of traditional statistics. We learn very early in our statistics training that the distribution of sample means, regardless of the shape of the parent distribution, approaches a normal distribution as the sample size increases. This fact permits us to use the normal distribution and distributions theoretically related to it, such as t, F, and χ2, for testing hypotheses about means and functions of means (such as the differences between two or more means, or variances, which are derived from means).
There is really nothing particularly “normal” about the normal distribution. ...