Normal Distribution

The normal distribution, also called the Gaussian distribution, is a continuous probability distribution for a real valued random variable whose probability density function forms the familiar symmetric bell shaped curve, centered on a mean value and spread according to a standard deviation. It is characterized completely by these two parameters, and the standard normal distribution is the special case with mean zero and standard deviation one. The distribution is named after Carl Friedrich Gauss, who used it to model errors in astronomical observations, though earlier work by Abraham de Moivre had already derived it as an approximation to the binomial distribution. Its central importance in statistics rests substantially on the central limit theorem, which shows that the sum of many independent random quantities tends toward a normal distribution regardless of the distribution of the individual quantities, which is why the normal distribution appears throughout the natural and social sciences to model measurement error, physical quantities and aggregated effects.