Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule to determine the following. A.) what percentage of people has an IQ between 64 and 136? B.) what percentage of people has an IQ score less than 76 or greater than 124? C.) what percentage of people has an IQ score greater than 112?

The Empirical Rule tells us that, in a normal or 'bell-shaped' distribution, 68% of the data is one standard deviation from the mean, 95% of the data is two standard deviations from the mean, and 99.7% of the data is three standard deviations from the mean.

A) 64 and 136 are 3 standard deviations away from the mean, so 99.7% of people have an IQ between 64 and 136.

B) 76 and 124 are 2 standard devations away from the mean, but the answer is asking what percentage is not between them. 100% - 95% gives us 5%.

C) 112 is one standard deviation away from the mean. If we want to find the percentage greater, then we can do 100% - 50% (as 112 is to the left of the mean), then we can take half of 68 to get 34%, and after subtracting 50% and 34% from the 100%, we get 16%.

joaobezerra joaobezerra · Answer 2 · 2021-09-17T21:00:25+02:00

Using the empirical rule, it is found that:

a) 99.7% of people has an IQ between 64 and 136.

b) 5% of people has an IQ score less than 76 or greater than 124.

c) 16% of people has an IQ score greater than 112.

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The Empirical Rule states that, for a bell-shaped(normal) distribution.

68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviations of the mean.
99.7% of the measures are within 3 standard deviations of the mean.

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In this question, mean of 100 and standard deviation of 12.

Item a:

64 = 100 - 3(12)

136 = 100 + 3(12)

Within 3 standard deviations of the mean, thus, 99.7%.

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Item b:

76 = 100 - 2(12)

124 = 100 + 2(12)

More than 2 standard deviations from the mean, thus 100 - 95 = 5%.

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Item c:

112 = 100 + 12

More than 1 standard deviation above the mean.

100 - 68 = 32% of the measures are more than 1 standard deviation from the mean.
The normal distribution is symmetric, which means that of these 32%, 16% are more than 1 standard deviation below and 16% are more than 1 standard deviation above.

Thus:

16% of people has an IQ score greater than 112.

A similar problem is given at https://brainly.com/question/15872420