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Atlantic Video, a small video rental store in Philadelphia, is open 24 hours a day, and - due to its proximity to a major business school - experiences customers arriving around the clock. A recent analysis done by the store manager indicates that there are 30 customers arriving every hour, with a standard deviation of interarrival times of 2 minutes. This arrival pattern is consistent and is independent of the time of the day. The checkout is currently operated by one employee, who needs on average 1.7 minutes to check out a customer. The standard deviation of this checkout time is 3 minutes, primarily as a result of customers taking home different numbers of videos.
If you assume that every customer rents at least one video (i.e. has to go to the check-out), what is the average time a customer has to wait in line before getting served by the check-out employee, not including the actual check-out time (in minute)?
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