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 $22$ 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 $$103.$ 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 $$212.$

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 a$-$level. Do not round intermediate

calculations. Round your answer to the nearest whole number.