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Queuing: Poison process

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The manager for Select-a-Seat, a company that sells tickets to athletic games, concerts, and other events, has determined that the number of people arriving at the Broadway location on a typical day is Poisson distributed with a mean of 12 per hours. It takes approximately 4 minutes to process a ticket request. Thus, if customers arrive in intervals that are shorter than 4 minutes, they will have to wait. Assuming that a customer has just arrived and the ticket agent is starting to serve that customer, what is the probability that the next customer who arrives will have to wait in line?

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Solution Summary

The solution gives the step-by-step procedure for waiting time distribution (see attachment).

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