A US airlines has determined that 5% of its customers do not show up for their flights. If a passenger is bumped off a flight the airline pays the customer $200. What is the expected payout of the airline, if it overbooks a 240 seat airplane by 5 percent?

Question

Savannah Anderson · Accepted Answer

#$0# Overbooks by #5%#, therefore #240 xx 1.05 = 252# passengers booked on the airplane. We then need to calculate #5%# of this, so #252 xx 0.05 = 12.6#. We then need to round this to #13# as you cannot have #0.6# of a person. #252 - 13 = 239# passengers to turn up to the flight. #239# people is less than #240# seats available, so the expected payout is #$0#.

Isaiah Anthony · Answer

#$0# Start by noting that the plane has 240 seats, and if the airline overbooked by #5%#, meaning that #105%# of the seats are booked, then #240*105%=240*1.05=252# seats were sold. Of these #252# tickets, #5%# of them will not be used, meaning that #100%-5%=95%# will be used. #252*95%=252*0.95=239.4~=240#. Since there are #240# passengers, no passengers, if everything goes according to average, no payout should be necessary.

Nathan Axel · Answer

undefined The expected payout of the airline can be calculated as follows:

1. Determine the total number of seats on the airplane after overbooking by 5%: 240 + (240 * 0.05) = 252 seats.
2. Calculate the number of passengers who do not show up for their flights: 252 * 0.05 = 12 passengers.
3. Multiply the number of bumped passengers by the payout amount: 12 * $200 = $2400.

So, the expected payout of the airline is $2400.