Suppose that the test score of a student taking the final of a probability course is a random variable with mean 79. (a) Give an upper bound for the probability that a student's test score will exceed 89. P{score > 89} < (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 22. What can you say about the probability that a student will score between 69 and 89 (do not use the central limit theorem)? P{69 score 89) 7 (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 79 (do not use the central limit theorem)? " (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? 11=