distribution and empirical rule

Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are at least 3.47 ?

Answer 1

3.47 - 2.61 = 0.86. So 3.47 is two standard deviations above the mean 2.61. Since we want to know the percentage that are at least 3.47, we want to know the percentage of data that is greater than 2 standard deviations above the mean. That would be 2.4% between 2 and 3 standard deviations and 0.15% above 3 standard deviations, for a total or 2.55%.