Twelve (12) machines are planned to be used for a 60-day production run for a major customer. The actual operating time is 1440 hours.

Upon failure, a machine must be returned to the manufacturer for repair. The turnaround time is at least 90 days and an average of 110 days.

The per machine failure rate is 0.01 failures per operating hour

(a) What is the expected number of machine failures during the production run?

(b) Determine the number of spare machines required so that the probability of exceeding this number is 5%.

(c) What is the probability that the number of spare machines required will exceed the expected number?

(d) What is the probability of no machine failure during 8 operating hours (a shift)?