Question

Assume that 75 was the mean test score on an exam, with a standard deviation of 4 points.

What percent had scores between 67 and 75? Use the % symbol in your answer.

Answer 1

68%

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 75, standard deviation of 4.

What percent had scores between 67 and 75?

67 = 71 - 4

75 = 71 + 4

Within 1 standard deviation of the mean, so, by the Empirical Rule, 68%.