Problem $20-5($Algo$)$

Next week, Super Discount Airlines has a flight from New York to Los Angeles that will be booked to capacity. The airline knows from past history that an average of $21$ customers $($with a standard deviation of $12)$ cancel their reservation or do not show for the flight. Revenue from a ticket on the flight is $$126.$ If the flight is overbooked, the airline has a policy of getting the customer on the next available flight and giving the person a free round$-$trip ticket on a future flight. The cost of this free round$-$trip ticket averages $$216.$ Super Discount considers the cost of flying the plane from New York to Los Angeles a sunk cost.

By how many seats should Super Discount overbook the flight?

Note: Use Excel's NORMSINV$()$ function to find the correct critical value for the given $-$level. Do not round intermediate calculations. Round your answer to the nearest whole number.

Overbook by

passengers