Standard normal distribution : A standard normal distribution is a normal distribution with mean 0 and standard deviation 1. The probability density of a standard normal distribution is given by $\frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}.$ The central limit theorem states the the sum of independent identically distributed random variables that is scaled to have a mean of 0 and a standard deviation of 1 converges towards a standard normal distribution.