### The average utilization of benny time

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Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of 2.0 per hour. It will take Benny an average of 18 minutes to give a haircut. Based on these figures, find the following:

a. The average number of customers waiting. (Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places.)

Average number of customers waiting

b. The average time a customer waits. (Round your answer to 2 decimal places.)

Average waiting time             minutes

c. The average time a customer is in the shop. (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.)

Average time             minutes

d. The average utilization of Benny’s time. (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.)

Average utilization             %

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