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- Bob runs a car oil change shop. His oil change crew can change the oil of a car in 10 minutes on average. Since he has only 1 oil change crew working on 1 oil change pit, only 1 car is processed at a time.Cars arrive at his oil change facility at the rate of 5.45 cars per hour. Assume the arrivals are Poisson distributed and the oil change service times by his crew follow an exponential distribution. Bob, after taking a class, has become interested in automation. He is thinking of investing in an automated robotic oil change unit that can replace his current crew. Bob learns that this automated robotic oil change machine takes precisely 10 minutes on every car to change the oil (i.e. there is no variability in this service time). Bob is a bit disappointed that this robotic oil change unit on average does not appear to be faster than his crew. Bob wants to reduce the customer waiting time at his shop. He wants you to help him figure out if the robotic oil change unit can reduce…Automobiles arrive at the drive-through window at a post office at the rate of 7 every 10 minutes. The average service time is 7 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.(Note: the given equations are NOT necessarily in the correct order.) What is the average time a car is in the system? What is the average number of cars in the system? What is the average time cars spend waiting to receive service? What is the average number of cars in line behind the customerreceiving service? What is the probability that there are no cars at the window? What percentage of the time is the postal clerk busy? What is the probability that there are exactly two cars in the system?