Z Distribution (Standard Normal)

The Z distribution (or standard normal distribution) function is determined by the following formula:

f(x) = 1/[(2p)1/2] * e**{-1/2*x2}

- < x <



is the base of the natural logarithm, sometimes called Euler's e (2.71...)


is the constant Pi (3.14...)

Note that this distribution is simply a normal distribution where the mean is zero and the standard deviation is one. The Z distribution is commonly used in hypothesis testing for large samples or in situations where the standard deviation is known.

This illustration shows various tail areas (or probabilities) of the Z distribution.

See also, Bivariate Normal Distribution, Elementary Concepts (Normal Distribution), Basic Statistics - Tests of Normality, Distribution Fitting - Normal Distribution, Q-Q Plots - Normal Distribution, and P-P Plots - Normal Distribution.

For a complete listing of all distribution functions, see Distributions and Their Functions.