At a car wash station, on average, there are 4 cars coming in for the service ev

Question

At a car wash station, on average, there are 4 cars coming in for the service every 10 minutes. The average wash time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. Please convert all rates into cars per hour and answer the following questions. Question 1 of 4 5.0 Points The average time a car spent in the waiting line is hours, and the total time a car spent in this car wash station is hour. (Please round to two decimal points and include no units.)

Explanation / Answer

Wash rate: 1 car/ 2 mins = 30 cars/ hour = µ Given: Poisson Process: Hence waiting time = (?/µ)/(µ-?) = (24/30) minutes/ (30-24) = 2/15 hours = 8 minutes = 0.133 hours Total time spent by car = 1/(µ-?) = 1/(30-24) = 1/6 hour = 10 minutes = 0.1667 hours

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