At a border inspection station, vehicles arrive at the rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion.

a. What is the average length of the waiting line?

b. What is the average time that a vehicle must wait to get through the system?

c. What is the utilization of the inspector?

d. What is the probability that when you arrive there will be three or more vehicles ahead of you?