### Customers arrive according to poisson distribution

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A tax accountant in a very small town has a walk-up tax preparation business in a small office. During “busy season”, she has determined that her customers arrive according to a Poisson distribution with an average arrival rate of 6 per day (it is a very small town). Each customer takes a number so that they may be served in the order of arrival. She is able to serve her customers one at a time, at an average rate of 8 per day (exponentially distributed). Her customers are very patient and will always wait as long as necessary to be served (the town is SO small, there’s nothing else to do). (15pts) What is the average time from arrival to exit? What is the average wait time for her customers? What is the average number of customers she has in her waiting room plus her office? What is the average number of customers waiting. How busy is our tax accountant during an average day? She has a small waiting room with 4 chairs. What is the probability that all chairs will be filled at the same time? If she works an 4 hour day, how many hours a day is she busy?

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