Laplace used the normal curve in 1783 to describe the distribution of errors . Subsequently, Gauss used the normal curve to analyze astronomical data in 1809. The normal curve is often called the Gaussian distribution. The term bell-shaped curve is often used in everyday usage. The normal distribution is the most used statistical distribution.
Normality is important in statistical inference.
The applet below plots the normal curve. The normal density is used to compute probabilities. The mean is a measure of location or center and the standard deviation is a measure of scale or spread. The image can be centered by clicking on the Rescale button. The standard normal random variable is denoted by Z as will be discussed later.