Question

Cars arrive at a parking lot at a rate of 20 per hour. Assume that a Poisson process model is appropriate. Answer the following questions. No derivations are needed but justification of your answers are necessary. What assumptions are necessary to model the arrival of cars as a Poisson process? What is the expected number of cars that arrive between 10:00 a.m and 11:45 a. m? Suppose you walk into the parking lot at 10:15 a.m.; how long, on average, do you have to wait to see a car entering the lot? Assume that the lot opens at 8 a.m. what is the expected time at which the ninth car arrives at the parking lot. What is the expected waiting time between the arrival of the 9th and 10th car? How is the waiting time between the arrival times of 9th and 10th car distributed? Write the density function of the waiting time. As an outsider, you watch the cars entering the parking lot for a half an hour in the morning (between 10 a.m and 10:30 a.m.) and then for a half an hour during the lunch time (between 1 p.m. and 1:30 p.m.). What can you say about the number of cars arriving at the parking lot during the two half hour periods? Suppose the probability that a car will need a handicapped parking spot is 1%, what is the expected number of cars needing handicapped spots between 10:00 am and 11:45 am?

Answer 1