Since I want to test out this new [ math ] thing anyways:

Suppose X_1,X_2,... is a sequence of i.i.d. random variables, each with mean \mu and variance \sigma^2, and let

S_n = \frac{1}{n} \sum_{i=1}^n X_i.

Then for each s,

P\left\{ \sqrt{n} \left(\frac{S_n-\mu}{\sigma} \right) \le s \right\}\to F_N(s)\quad\text{as}\quad n\to\infty

where

F_N(s) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^s e^{-t^2/2} dt

is the cumulative distribution function of the N(0,1) distribution.