Steve Austin is the fleet manager for SharePlane, a company that sells fractional ownership of private jets. SharePlane must carefully maintain their jets at all times. If a jet breaks down, it must be repaired immediately. Even if a jet functions well, it must be maintained at regularly scheduled intervals. Currently, Steve is managing two jets, Jet A and Jet B, for a collection of clients and is interested in estimating their availability in between trips to the repair shop as having both jets out-of-service due to repair or maintenance at the same time can affect its customer service. Jet A and Jet B have just completed preventive maintenance. The next maintenance is scheduled for both Jet A and Jet B in four months. It is also possible that one or both will break down  before this scheduled maintenance and require repair. The amount of time to a plane’s first failure is uncertain. Historical data recording the time to a plane’s first failure (measured in months) is provided in the TimeToFailData worksheet of the file TwoJets. Determine an appropriate probability distribution for these data. Furthermore, once a plane enters repair (either due to a failure or as scheduled maintenance), the amount of time the plane will be in maintenance is also uncertain. Historical data recording the repair time (measured in months) is provided in the RepairTimeData worksheet of the file TwoJets. Examine the appropriateness of fitting a log-normal distribution to these data. Steve wants to develop a simulation model to estimate the length of time that Jet A and Jet B are both out-of service over the next few months. For simplicity, you can assume that these planes will enter repair or maintenance just once over the next few months.

a. What is the average amount of time that the planes are both out-of service?
b. What is the probability that the planes are both out-of-service for longer than 1.5 months?