Question: I need your help understanding the material so I can score high on my upcoming test. Single-server Model Arrivals Exit Scenario: A small auto repair

I need your help understanding the material so I can score high on my upcoming test.

I need your help understanding the material so I

Single-server Model Arrivals Exit Scenario: A small auto repair shop has one mechanic that is dedicated to the installation of new mufflers. Customers arrive for a new muffler on average every 30 minutes. The mechanic can install mufflers on average at the rate of 3 per hour. Assume this service can be modeled as a single- server model. Mechanic's Service 1. On average, how many cars are in the system? 2. On average, how many cars are in the waiting line? Show your answer to two decimals. 3. On average, how long does a car spend waiting in the line? 4. How many minutes each hour is the mechanic idle (that is, not busy)? 5. What is the probability that you arrive at the shop for a new muffler and you do not have to wait to be serviced? 6. Suppose the manager of the auto repair shop wants to reduce the amount of time a car spends in the system for a muffler installation by two-thirds. To accomplish this, what service rate will be required of the mechanic? Show your answers as cars per hour. Single-server Model Arrivals Exit Scenario: A small auto repair shop has one mechanic that is dedicated to the installation of new mufflers. Customers arrive for a new muffler on average every 30 minutes. The mechanic can install mufflers on average at the rate of 3 per hour. Assume this service can be modeled as a single- server model. Mechanic's Service 1. On average, how many cars are in the system? 2. On average, how many cars are in the waiting line? Show your answer to two decimals. 3. On average, how long does a car spend waiting in the line? How many minutes each hour is the mechanic idle (that is, not busy)? 5. What is the probability that you arrive at the shop for a new muffler and you do not have to wait to be serviced? 6. Suppose the manager of the auto repair shop wants to reduce the amount of time a car spends in the system for a muffler installation by two-thirds. To accomplish this, what service rate will be required of the mechanic? Show your answers as cars per hour

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