g A particular IQ test is standardized to a Normal model, with a mean of 100 and a standard deviation of 18. Using the empirical rule, about what percent of people should have IQ scores above 118 ?

Question

Mathematics

Mccarthy

4 March, 20:17

g A particular IQ test is standardized to a Normal model, with a mean of 100 and a standard deviation of 18. Using the empirical rule, about what percent of people should have IQ scores above 118 ?

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Answers (1)

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Drake Haney · Answer 1

About 16% percent of people should have IQ scores above 118 .

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 100

Standard deviation = 18

Using the empirical rule, about what percent of people should have IQ scores above 118 ?

118 = 100 + 18

By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean, that is, between 82 and 118. The other 32% is more than 1 standard deviation from the mean. Since the normal distribution is symmetric, 16% are below 82 and 16% are above 118

So

About 16% percent of people should have IQ scores above 118 .