bell shape distribution

Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.51 and a standard deviation of 0.41. Using the empirical rule, what percentage of the students have grade point averages that are less than 1.69?

Answer 1

1.69 is (2.51 - 1.69)/0.41 = 2 standard deviations below the mean. Per the empirical rule 2.4% of the data is less than 2 standard deviations below the mean.