Question: 1. (7 points) Use queueing theory. Mike Jones, the mechanic at Extreme Muffler Shop, is able to install new muffler at an average rate of

1. (7 points) Use queueing theory. Mike Jones,

1. (7 points) Use queueing theory. Mike Jones, the mechanic at Extreme Muffler Shop, is able to install new muffler at an average rate of 6 per hour (or about 1 in every 10 minutes), according to an exponential distribution. Customer seeking this service arrive at the shop on the average of 3 per hour, following a Poisson distribution. They are served on a FCFS basis and come from a very large population of possible byers. Obtain the operating characteristics of Extreme Muffler Shop's queueing system by answering the following. a. What is the average time a car is in the system? b. What is the average number of cars in the system? c. What is the average number of cars waiting to receive service? d. What is the average time a car is in the queue? e. What is the probability that there are no cars in the system? f. What percent of the time the mechanic is busy? g. What is the probability that there are exactly 2 cars in the system

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