Question

Scores of an IQ test have a bell shaped distribution with a mean of 100 and a standard deviation of 20 use the empirical rule determine the following what percentage of people have an IQ score less than 60 or greater than 140

Answer 1

5% of people have an IQ score less than 60 or greater than 140

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 = 20

What percentage of people have an IQ score less than 60 or greater than 140

60 = 100 - 2*20

So 60 is two standard deviations below the mean

140 = 100 + 2*20

So 140 is two standard deviations above the mean

By the Empirical Rule, 95% of the people have an IQ between 60 and 140, and 5% have an IQ outside this range, that is, less than 60 or greater than 140.