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Question
NARRBEGIN: SA_85_88The College of Arts and Sciences at a Midwestern university currently has three parking lots, each containing 160 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, the probability of a lot 1 parking sticker holder showing up is 73%, a lot 2 parking sticker holders showing up is 75%, and a lot 3 parking sticker holder showing up is 77%.
NARREND
(A) What are the appropriate probability distributions to model the number of faculty members showing up in each lot?
(B) Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a parking space. Assume that the number who shows up at each lot is independent of the number who shows up at the other two lots.
(C) Suppose that faculty members are allowed to park in any lot. Does this help solve the problem? Why or why not?
(D) Suppose that the numbers of faculty who show up at the three lots are correlated, with each correlation equal to 0.80. Does your answer to (C) change? Why or why not?
Answer
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