Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.542.54 and a standard deviation of 0.420.42. Using the empirical rule, what percentage of the students have grade point averages that are between 1.281.28 and 3.83.8?

By the Empirical Rule, 99.7% of the students have grade point averages that are between 1.28 and 3.8.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) 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 = 2.54

Standard deviation = 0.42.

Between 1.28 and 3.8?

1.28 = 2.54 - 3*0.42

So 1.28 is 3 standard deviations below the mean

3.8 = 2.54 + 3*0.42

So 3.8 is 3 standard deviations above the mean

By the Empirical Rule, 99.7% of the students have grade point averages that are between 1.28 and 3.8.