The management of Quality Airlines has decided to base its overbooking policy on the overbooking model presented in Sec. 18.8. This policy now needs to be applied to a new flight from Seattle to Atlanta. The airplane has 125 seats available for a nonrefundable fare of $250. However, since there commonly are a few no-shows on similar flights, the airline should accept a few more than 125 reservations. On those occasions when more than 125 arrive to take the flight, the airline will find volunteers who are willing to be put free on a later Quality Airlines flight that has available seats, in return for being given a certificate worth $500 (but that would cost the company just $300) toward any future travel on this airline. Management feels that an additional $300 should be assessed for the intangible cost of a loss of goodwill for inconveniencing these customers.
Based on previous experience with similar flights having about 125 reservations, it is estimated that the relative frequency of the number of no-shows (independent of the exact number of reservations) will be as shown below.
Number of No-Shows Relative Frequency
0.............. 0%
1............... 5
2.............. 10
3.............. 10
4.............. 15
5.............. 20
6.............. 15
7.............. 10
8.............. 10
9.............. 5
Instead of using the binomial distribution, use this distribution directly with the overbooking model to determine how much overbooking the company should do for this flight.