standard deviation

Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5 and a standard deviation of 0.45. Using the empirical rule, what percentage of the students have grade point averages that are no more than 3.85? Please do not round your answer.

Answer 1

3.85 is 3 standard deviations above the mean, as (3.85-2.5)/.45 = 3

The empirical is normally stated that 99.7% are within 3 standard deviations of the mean. For the percent less than 3 sd, we have to add back in the number less than -3 sd deviations. This is where you have to read the minds of the person posing the question, as 1/2 of .3% is .15%, so 99.7% + .15% = 99.85%.