Central Limit Theorem

Let $Y_1,Y_2,\dots ,Y_N$ be independent, identically distributed random variables with mean $\mu$ and variance ${\sigma }^2$. Then

$$\frac{\left(\frac{1}{N}{\sum }_{n=1}^N{Y}_N\right)-\mu }{\sigma /\sqrt{N}}\to Z\sim N(0,1)$$

or the standard normal.