Question

Because many passengers who make reservations do not show​ up, airlines often overbook flights​ (sell more tickets than there are​ seats). A certain airplane holds 104 passengers. If the airline believes the rate of passenger​ no-shows is 9​% and sells 116 ​tickets, is it likely they will not have enough seats and someone will get​ bumped?

1) Use the normal model to approximate the binomial to determine the probability of at least 105 passengers showing up.

2) Should the airline change the number of tickets they sell for this​ flight? Explain

Answer 1

Let X = No. of passengers showing up.

X follows Binomial distribution with parameter n = 116 and p = 1-0.09 = 0.91 (Because probability that passenger​ no-shows is 9​%).

Hence,

Thus X follows normal distribution with parameter

1.

2.

If airline sell 116 tickets then probability that at least 105 passenger shows up for this flight is 0.6346 which is very high, hence the airline should change the number of tickets they sell for this​ flight.