The Normal disribution is widely used in
statistical analysis, due to its well-defined properties. The Normal distribution is assumed in many tests of statistical inference, such as
hypothesis tests, as well as ANOVA.
Tests for normality of residuals is standard practice in regression analysis as a means to verify fit of the regression model.
Normality is also assumed when plotting individuals data (n=1) on a standrd Individual-X control chart.
(see Defining Control Limits).