Suppose that you have a set of $n$ independent and identically distributed random variables, $\{ X_i \}$ with finite mean $\mu$ and variance $\sigma^2$. Let $S_n$ denote the sum of the random variables, $$ S_n = X_1 + X_2 + ... + X_n. $$ The Central Limit Theorem states that the random variable $$ G_n = \frac{S_n - \mu n}{\sigma \sqrt{n}} $$ converges to a standard normal distribution in the limit of $n$ going to infinity $$ \lim_{n \rightarrow \infty} G_n = N(0,1). $$