Many statistical tests and procedures assume that data follows a normal (bell-shaped) distribution.

For example, all of the following statistical tests, statistics, or methods assume that data is normally distributed:

- Hypothesis tests such as t-tests, Chi-Square tests, F tests
- Analysis of Variance (ANOVA)
- Least Squares Regression
- Control Charts of Individuals with 3-sigma limits
- Common formulas for process capability indices such as C
_{p}and C_{pk}