Cars traveling from Canada to the United States through the Thousand Islands Border Crossing must stop for US Customs and Immigration. During the stop, each passenger in the car must present a passport for inspection by a US Customs Officer, answer questions, and declare certain valuables that may be in the car. On average, it takes a customs officer about 8 minutes to inspect passports and release a car for entry into the United States. Since the Thousand Islands Border Crossing is not heavily trav- eled at night, US Customs and Immigration keeps only one lane open at the check- point plaza and one officer on duty to process arriving cars. Between midnight and 6:00 a.m., cars arrive at the Border Crossing plaza at an average rate of five an hour.

a. Assuming this scenario meets the assumptions of the M/M/1 model, how busy is this customs officer during that time period?

b. What is the average wait to speak to that officer? What is the probability that someone is able to speak to the officer immediately upon arrival?

c. On average, how many cars are present at the Thousand Islands Border Crossing plaza during that time period?