Please answer clearly and show mathematics, dont post old solutions.

Turkish Airlines has a flight from Ankara to Istanbul that will be booked to capacity next week. The airline knows from past history that the number of customers who cancel their reservation or do not show up for the flight is normally distributed with a mean of 20 and a standard deviation of 5. Revenue from a ticket on the flight is 1250 TL. 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 is 2400 TL. Turkish Airlines considers the cost of flying the plane from Ankara to Istanbul a sunk cost. The plane has 200 seats.

(a) (10 points) By how many seats should the airline overbook the flight?

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