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Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The shop consists of a small garage and an adjacent parking lot. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege.
1) How long (in minutes) do vehicles wait on average exclusively in the adjacent parking lot?
2) What is the average number of vehicles one would expect to find exclusively in the garage? (In other words, at any given time what is the probability of finding a vehicle in the garage?)
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