Question

Intelligence quotients (IQs) on the Stanford-Binet intelligence test are normally distributed with a mean of 100 and a standard deviation of 16.

Use the 68-95-99.7

Rule to find the percentage of people with IQs between 84 and 116.

Answer 1

Approximately 68% of people have IQs between 84 and 116.

Explanation:

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

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

Approximately 95% of the measures are within 2 standard deviations of the mean.

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

In this problem, we have that:

Mean of 100, standard deviation of 16.

Percentage of people with IQs between 84 and 116.

84 = 100 - 16

116 = 100 + 16

So within 1 standard deviation of the mean, which, by the Empirical Rule, is approximately 68%.