Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 2.13 and 2.99

Answer 1

Approximately 68% of the students have grade point averages that are between 2.13 and 2.99.

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 question, we have that:

Mean = 2.56

Standard deviation = 0.43

What percentage of the students have grade point averages that are between 2.13 and 2.99?

2.56 - 0.43 = 2.13

2.56 + 0.43 = 2.99

Within one standard deviation of the mean, so, by the Empirical Rule:

Approximately 68% of the students have grade point averages that are between 2.13 and 2.99.