Exam Scores. Consider the following sample of exam scores, arranged in increasing order.

28 57 58 64 69 74 79 80 83 85 85 87 87 89 89 90 92 93 94 94 95 96 96 97 97 97 97 98 100 100 The sample mean and sample standard deviation of these exam scores are 85 and 16.1, respectively. Modeling your solutions after those in Example 3.15 on pages 139–140, solve the following problems.

a. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given by Chebyshev’s rule with k = 2.

b. Repeat part

(a) with k = 3.

c. Interpret your results from parts

(a) and (b).