Question

Offwefly Airlines has a daily flight from Sacramento to Las Vegas with a capacity of 100 passengers. On average, 18 ticket holders cancel their reservations at the last minute, so the company intentionally overbooks the flight. Cancellations can be described by a normal distribution with a standard deviation of 2.2. Profit per passenger is $189. If a passenger arrives but cannot board due to overbooking, the company policy is to provide compensation of $131. What is the optimal probability of having too many passengers to seat on the plane? Carry answer to 4 decimal places.

Answer 1

Underage cost = Cu = profit per passenger = $189

Overage cost = Co = cash payment per passenger = $ 131

Thus , Critical ratio = Cu / Cu + Co = 189 / ( 189 + 131) = 189 / 320 = 0.5906

Corresponding Z value for above Critical Ratio = NORMSINV ( 0.5906) = 0.2291( 0.23 ROUNDED TO 2 DECIMAL PLACES )

Thus, number of tickets to be overbooked

= Mean value of cancellation + Z x Standard deviation of cancellation

= 14 +0.23 x 2.2

= 14 +0.506

= 14.506 ( 15 rounded to nearest whole number )

OVERBOOKED = 15 TICKETS