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Marty's Barber Shop has one barber. On average, every 25 minutes one customer arrives to the store and it takes 10 minutes to complete one

Marty's Barber Shop has one barber. On average, every 25 minutes one customer arrives to the store and it takes 10 minutes to complete one haircut. The waiting line model assumptions of Poisson arrivals and exponential service times appear reasonable for this service system. Marty is concerned to lose his customers to the new barbershop in the neighborhood. Answer to the following questions to help Marty assess his business performance.

  1. What percentage of the customers will take less than 12 minutes to receive service?
  2. What is the total probability of receiving exactly 1 or exactly 2 customers in half an hour?

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