Presume X is a random variable from a distribution with known mean \(\mu\) and known variance \(\sigma_x^2\text{.}\) For some natural number n, sample the distribution repeatedly creating a string of random variables denoted \(X_1, X_2, ... , X_n\) and set \(\overline{X} = \frac{\sum X_k}{n}\text{.}\)

Then, \(\overline{X}\) is approximately normally distributed with mean \(\mu\) and variance \(\sigma^2 = \frac{\sigma_x^2}{n}\text{.}\)