Question

In a standardized IQ test, the mean score is 100 and the standard deviation is 15. According to the Empirical rule, 95 % of all those who took the test should have scores between________________

Answer 1

According to the Empirical rule, 95 % of all those who took the test should have scores between 70 and 130.

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 = 15

According to the Empirical rule, 95 % of all those who took the test should have scores

Within 2 standard deviations of the mean

100 - 2*15 = 70

100 + 2*15 = 130

According to the Empirical rule, 95 % of all those who took the test should have scores between 70 and 130.