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Chapter 9: The Normal Probability Distribution
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Note:
All application problems involving the normal distribution can be reduced to
simpler problems using z-scores. These reduced problems can be solved in
the same way as the previous examples or combinations of them.
However, in this section we will only use the
Normal
and
Inverse Normal
Distribution
workbooks since the procedures in them will work for any
normal variable. That is, it does not matter what are the values of the mean
and standard deviation for the normal variable, we will be able to use these
workbooks for the necessary computations. These workbooks are not
restricted to the standard normal random variable.
Example 9-10
:
An
intelligence quotient, or IQ, is a score derived from
one of several different standardized tests designed to evaluate intelligence.
Research has shown that IQ scores can be modeled with a normal
distribution.
If IQ scores are normally distributed with a mean of 100 and a
standard deviation of 15, what is the probability that a person chosen at
random from the population at large will have an IQ score greater than 109?
Solution:
Let
X
= IQ score. Then the random variable
X
will be normally
distributed with a mean of 100 and a standard deviation of 15. Based on the
problem, we need to find
P
(
X
109). Using the
Normal Probability
Distribution
workbook to solve, we get
the value of 0.2743. The result is
shown in
Figure 9-34
.
Based on this information, we can expect about 27.43% of the general
population to have an IQ score of at least 109.