The exam scores for a particularly difficult math test had a mean score of 75% with a standard deviation of 8%. Approximately what percentage of the class scored between a 67% and an 83%.

Question

The exam scores for a particularly difficult math test had a mean score of 75% with a standard deviation of 8%. Approximately what percentage of the class scored between a 67% and an 83%.

Answer 1

mean = 75

sd = 8

what percent between 83 and 67?

(83-75)/8 = 1 = z score

34% are between 75 and 83

(67-75)/8 = -1 = z score

34% are between 67 and 75

68% are within 1 standard deviation from the mean

68% are between 67 and 85, by the empirical rule

for a closer approximation, use z tables or a z calculator