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 < ∞
where
e |
is the
base of the natural logarithm, sometimes called Euler's e (2.71...) |
p |
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.