Recreational boats arrive at a single gasoline pump located, Basic Statistics

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Recreational boats arrive at a single gasoline pump located

Question: Recreational boats arrive at a single gasoline pump located at the dock at Trident Marina at an average rate of 10 per hour on Saturday mornings. The fillup time for a boat is normally distributed, with an average of 5 minutes and a standard deviation of 1.5 minutes. Assume that the arrival rate follows the Poisson distribution.

(a) What is the probability that the pump is vacant?

(b) On average, how long does a boat wait before the pump is available?

(c) How many boats, on average, are waiting for the pump?

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