Note: Each numbered question is worth 20 points. For maximum credit, show all ne

Question

Note: Each numbered question is worth 20 points. For maximum credit, show all necessary work and include all computer files you use.

Cars arrive at a parking lot at a rate of 52 per hour according to some distribution. You only know that the times between arrivals are independent. Also, the time a car spends in the lot has an independent distribution with a mean of 48 minutes. The lot has room for 40 cars. a. What is the probability that an arriving car will not be able to find an available space? (Assume people do not wait for a space if one is not immediately available) b. What is the average number of cars in this parking lot?

Explanation / Answer

Solution:

Given that = 52/hr
1/ = 48 mins = 48/60 hrs
= (5/4)/hr = (5/4)* 52 = 62.5
p = (/) = 52/62.5 = 0.832
q = (1-p) = 1-0.832 = 0.168
Ls = p/1-p = 0.832/0.168
Ls = 4.956

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