The Normal Distribution Model

A continuous random variable x has a normal distribution with certain parameters ji (mean, parameter of location) and a2 (variance, parameter of spread) if its density function is given by the following equation  

To compute parameter independent tables one transforms x into a standardized random variable u  

In practice, most real random variables which are empirically sampled to provide a limited number of observations do not normally represent exactly normally distributed variables. 

The analyst who does not usually worry about the real distribution of a set of results should at least be sure that succeeding computations and tests are not significantly affected by violations of the assumption of a special distribution. Otherwise he may 

---