Question: The Acme Machine Shop has five machines that periodically break down and require service. The average time between breakdowns is 4 days, distributed according to

The Acme Machine Shop has five machines that periodically break down and require service. The average time between breakdowns is 4 days, distributed according to an exponential distribution.
The average time to repair a machine is 1 day, distributed according to an exponential distribution. One mechanic repairs the machines in the order in which they break down.
a. Determine the probability that the mechanic is idle.
b. Determine the mean number of machines waiting to be repaired.
c. Determine the mean time machines wait to be repaired.
d. Determine the probability that three machines are not operating (are being repaired or waiting to be repaired).

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