Problem $11-5($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

history that an average of $28$ customers $($with a standard deviation of $14)$ cancel their reservation or do not show for the flight. Revenue

from a ticket on the flight is $$122.$ 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 $$228.$ 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 NORM.S$.$INV$()$ function to find the $z$ value. Round $z$ value to $2$ decimal places. Round your answer to the nearest

whole number.

Overbook by