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Exercise 11.2.5 Customers arrive at Bunkey’s car wash service at a rate of one every 20...

Exercise 11.2.5 Customers arrive at Bunkey’s car wash service at a rate of one every 20 minutes and the average time it takes for a car to proceed through their single wash station is 8 minutes. Answer the following questions under the assumption of Poisson arrivals and exponential service.

(a) What is the probability that an arriving customer will have to wait?

(b) What is the average number of cars waiting to begin their wash?

(c) What is the probability that there are more than five cars altogether?

(d) What is the probability that a customer will spend more than 12 minutes actually waiting before her car begins to be washed?

(e) Bunkey is looking to expand and he can justify the creation of a second wash station so that two cars can be washed simultaneously if the average time spent waiting prior to service exceeds 8 minutes. How much does the arrival rate have to increase in order for Bunkey to justify installing this second wash station?

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