Question $2$

Next week, Super Discount Airlines has a fight from New York to Los Angeles that will be booked to full capacity. The airline knows from past history that an average of $20$ customers $($with a standard deviation of $10)$ cancel their reservation or do not show for the finue from a ticket on the fight is $$125.$ If the fight is overbooked, the airline has a policy of getting the customer on the next available flight and giving the person a free round$-$trip ticket on a future fight. The cost of this free round$-$trip ticket averages $$250.$ Super Discount considers the cost of flying the plane from New York to Los Angeles a sunk cost.

a$)$ By how many seats should Super Discount overbook the fight?

b$)$ FAA is planning to mandate minimum $$500$ compensation for those passengers lost seats due to overbooking. How will this new regulation affect the overbook seat for this flight?

Note: NORMSINV$(0\mathrm{.}33)=-0\mathrm{.}43,$ NORMSINV$(0\mathrm{.}67)=0\mathrm{.}43,$ NORMSINV$(0\mathrm{.}5)=0\mathrm{.}00,$ NORMSINV$(0\mathrm{.}2)=-0\mathrm{.}84,$ NORMSINV$(0\mathrm{.}8)=0\mathrm{.}84$