Question

Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 16 seconds. Thus, 99.7% of running times are approximately between:

A. 61 and 125 seconds

B.77 and 109 seconds

C. 45 and 141 seconds

D. None of the answer options is correct

Answer 1

C. 45 and 141 seconds

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 = 93 seconds

Standard deviation = 16 seconds

99.7% of running times are approximately between:

By the Empirical rule, within 3 standard deviations of the mean, so between 3 standard deviations below the mean and 3 standard deviations above the mean

3 stnadard deviations below the mean

93 - 3*16 = 45 seconds

3 standard deviations above the mean

93 + 3*16 = 141 seconds

The correct answer is:

C. 45 and 141 seconds