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Chapter 9: The Normal Probability Distribution
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special normal distribution, called the
standard normal distribution
to
simplify this situation.
Definition: Standard Normal Distribution
The standard normal distribution is a normal distribution with a mean of 0
and a standard deviation of 1.
Note:
Any normal random variable can be converted to a standard normal random
variable by computing the corresponding z-score.
The
z-
score for a normal random variable
X
is computed from the following
formula:
In the equation to compute the
-score,
is the value of a normal random
variable
X
, with mean
and standard deviation
.
Note:
The z-score is a random variable that is normally distributed with a mean of
0 and a standard deviation of 1.
Recall that a
-score gives the number of standard deviations a specific
value in the distribution is above or below the mean.
Extensive tables can be constructed for the standard normal random variable
to aid in finding areas (probabilities) under the standard normal curve.
Usually, standard normal tables give the area between the mean of 0 and a
value
, as shown in
Figure 9-16
. Since there is an infinite number of