Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100100 and a standard deviation of 1414. Use the empirical rule to determine the following. ​(a) What percentage of people has an IQ score between 7272 and 128128​?

Answer 1

95% of people have an IQ score between 72 and 128.

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 = 14.

​(a) What percentage of people has an IQ score between 72 and 128​?

72 = 100 - 2*14

So 72 is two standard deviations below the mean.

128 = 100 + 2*14

So 128 is two standard deviations above the mean.

By the Empirical Rule, 95% of people have an IQ score between 72 and 128.