15. From past experience, a professor knows that the test score of students taking a nal examination is a random variable with mean 65. (a) Give an

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15. From past experience, a professor knows that the test score of studentstaking a final examination is a random variable with mean 65. (a) Give an upper bound on the probability that a student's test scorewill exceed 75. (b) Suppose 1n addition the professor knows that the variance of astudent's test score is equal to 30. What can be said about theprobability that a student will score between 55 and 75? (c) How many students would have to take the examination so as to ensure, with probability at least 0.8, that the class average would bewithin 5 of 65?