Central limit theorem : The central limit theorem states that the distribution of $\frac{(\sum_{k=1}^{n}X_i)-n\mu}{\sqrt{n}\sigma}$ will converge to a standard normal distribution for $n$ approaching $\infty$ for independent identically distributed random variables $X_1, X_2,\ldots$ with mean $\mu$ and standard deviation $\sigma.$ The interpretation is that the sum of a large number of small random factors will approximately have a normal distribution.