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Utilization Rates, Down Times, and Probabilities

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19. "Fast Eddie" Flournoy manages the service equipment division of Delta Airline's Atlanta terminal. He keeps a service crew on call to repair tow tractors that break down. Tractors break down on an average of three per day. The repair crew could service an average of 8 tractors per day. "Fast Eddie", a real math whiz, estimates that the occurrence of the failures is Poisson in nature and the repair time distribution resembles an exponential distribution (see attachment).

a. What is the utilization rate of this service system?

b. What is the average down time for a broken tractor?

c. What is the probability that there will be 2 down tractors in the system?

d. If "Fast Eddie" observes that the on call crews are idle about 50% of the time is he safe in assuming that they are not doing their job? Why do you so state?