Show all necessary work and include all computer files you use. Cars arrive at a
ID: 3233668 • Letter: S
Question
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
Average number of cars serviced in the parking lot in one hour = 40*60/48=50 cars.
Probability that arriving car will not be able to find space = (52-50)/52 = 2/52 = 0.0384
Average no. of cars in parking lot = Min(40, 52*60/48) = 40 cars