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

$1\mathrm{.}5$ months?

$22.$ Blackjack Card Game.