Suppose that the test score of a student taking the final of a probability course is a random variable with mean 77. (a) Give an upper bound for the probability that a student's test score will exceed 87. P{sc0re > 87} S (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 27. What can you say about the probability that a student will score between 67 and 87 (do not use the central limit theorem)? P{67 3 score 3 87} >= v (c) How many students would have to take the final to ensure with a probability of at least 0.9 that the class average would be within 5 of 77 (do not use the central limit theorem)? ma