[15 points] The move to online instruction that was forced on universities by COVID has introduced considerable uncertainty in demand for face to face instruction. A business school is trying to decide how many face to face sections of an introductory accounting course need to be offered in the coming semester, and has come up with the following probability distribution for demand. Number of students who will choose to Prob(x) attend in person (X) 200 10 250 .20 300 40 350 15 400 15 a. Is this a valid probability distribution? Why or why not? "b. What is the expected value and standard deviation of the number of students who will choose to attend in person? c. Would you say the distribution above obeys the empirical rule? Justify briefly either way. d. Regardless of whether you answered yes or no to (c), assume the empirical rule applies. If you were the accounting department chair, what range of values of x would you use to plan how many face-to-face sections to offer? Justify briefly