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 fill up 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?