Question

Each of Gateway Airlines’ planes has 10 seats in its first-class cabin. Gateway’s overbooking policy on their flight from Boston to NYC is to sell up to 15 first-class tickets since no-shows are somewhat frequent on such a short route.

Let X represent the number of first-class tickets sold on a flight, where each ticket has a 90% chance of being sold. Suppose there is a 30% chance that a passenger who bought a ticket does not show up; let Y represent the number of passengers who show up for their flight.

Let Z represent the number of passengers who will not have a seat; for example, if 12 passengers bought tickets and show up, then 2 passengers will need to be bumped from the flight and compensated for their trouble.

1. a) What is the average number of first-class tickets sold, and with what standard deviation?

2. b) Calculate and interpret E(Y |X = 10).

3. c) Any assumptions required to make the calculations in parts a) and b)? Why?

4. d)   Possible values Z takes on, relative to the possible values of Y.

Answer 1