Standard Normal Distribution
Prerequisites
Effects
of Linear Transformations, Introduction
to Normal Distributions
Learning Objectives
 State the mean and standard deviation of the standard normal distribution
 Use a Z table
 Use the normal calculator
 Transform raw data to Z scores
A normal distribution with a mean of 0 and a standard
deviation of 1 is called a standard
normal distribution.
Areas of the normal distribution are often represented
by tables of the standard normal distribution. A portion of a
table of the standard normal distribution is shown in Table 1.
The first column titled "Z" contains
values of the standard normal distribution; the second column
contains the area below Z. Since the distribution has a mean of
0 and a standard deviation of 1, the Z column is equal to the
number of standard deviations below (or above) the mean. For example,
a Z of 2.5 represents a value 2.5 standard deviations below the
mean. The area below Z is 0.0062.
Calculate
Areas
A value from any normal distribution can be transformed
into its corresponding value on a standard normal distribution
using the following formula:
Z = (X  μ)/σ
where Z is the value on the standard normal distribution,
X is the value on the original distribution, μ is the mean
of the original distribution and σ is the standard deviation
of the original distribution.
If all the values in a distribution are transformed to Z scores,
then the distribution will have a mean of 0 and a standard distribution.
This process of transforming a distribution to one with a mean
of 0 and a standard deviation of 1 is called standardizing
the distribution.
