Airlines routinely overbook flights to compensate for people who don’t show up. An empty seat on a plane means a loss of revenue to an airline. Suppose that for a small plane with 25 seats, an airline takes 27 reservations. Define the random variable X as the number of people who actually show up for a sold-out flight. From past experience, the probability distribution of X is given below values of X 22 23 24 25 26 27 p(x) 0.05 0.15 0.24 0.37 0.12 0.07 A started Excel file is provided in the lab folder. This file may be helpful when completing this lab.

(f) If the Airplane does not have enough seats (either 26 or 27 passengers show up for their flight) the airline will offer customers an offer worth $800 to take a different flight later in the day. This offer is given on a first come first serve bases only up to the number of seats needed. Assume that all 27 customers pay $500 for their ticket at purchase regardless of whether they show up for their flight or not. Further assume the flight has a fixed operating expense of $11000. Here we will assume: Profit = Total income - variable cost - fixed expenses.

i. In this scenario what is the expected profit (or mean profit) from this flight assuming they sell 27 tickets?

ii. If the airline didn’t offer any additional tickets over the number of seats what would their expected profit have been?

iii. Based on your answer to parts (1(f)i and 1(f)ii) do you think they made a wise decision to sell 27 tickets even though there are only 25 seats