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 0.38. Using the empirical rule, what percentage of the students have grade point averages that are greater than 1.8?

Answer 1

Given that, mean = 2.56

standard deviation = 0.38

By Empirical rule, approximately 95% of the data fall within 2 standard deviations of the mean. That is 95% of the students have grade point averages that are between 1.8 and 3.32

Therefore, 100 - 95 = 5% of the data fall outside the 2 standard deviations of the mean.

And 5/2 = 2.5% of the data fall below 1.8 and fall above 3.32

Hence, 95 + 2.5 = 97.5% of the students have grade point averages that are greater than 1.8

Answer : 97.5%