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 $27$ customers $($with a standard deviation of $17)$ cancel their reservation or do not show for the flight. Revenue from a ticket on the flight is $\backslash (\backslash$$ $118\backslash ).$ If the flight is overbooked, the airline has a policy of getting the customer on the next available flight and giving the person a free round$-$trip ticket on a future flight. The cost of this free round$-$trip ticket averages $\backslash (\backslash$$ $235\backslash ).$ 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 $\backslash ($ a $\backslash )-$level. Do not round intermediate calculations. Round your answer to the nearest whole number.