# The Central Limit Theorem

Given a population with mean, $\mu$, and standard deviation, $\sigma$, the distribution of sample means taken from this population (of size $n$ and with replacement) becomes more normal as $n$ increases.

Further, the mean and standard deviation of this distribution of sample means are given by:

$$\mu_{\overline{x}} = \mu \quad \textrm{ and } \quad \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$$