The U.S. Army Engineering and Housing Support Center recently sponsored a study of the reliability, availability, and maintainability (RAM) characteristics of small diesel and gas-powered systems at commercial and military facilities (IEEE Transactions on Industry Applications, July/Aug. 1990). The study revealed that the time, Y, to perform corrective maintenance on continuous diesel auxiliary systems has an approximate exponential distribution with an estimated mean of 1,700 hours.

a. Assuming μ = 1,700, find the probability that the mean time to perform corrective maintenance for a sample of 70 continuous diesel auxiliary systems exceeds 2,500 hours.

b. If you observe Y̅ > 2500, what inference would you make about the value of μ?