In: Statistics and Probability
Based on long experience, an airline found that about 8% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats.
(a) What is the probability that a person holding a reservation
will show up for the flight?
(b) Let n = 267 represent the number of ticket
reservations. Let r represent the number of people with
reservations who show up for the flight. What expression represents
the probability that a seat will be available for everyone who
shows up holding a reservation?
P(r ≥ 255)P(r ≥ 267) P(r ≤ 255)P(r ≤ 267)
(c) Use the normal approximation to the binomial distribution and
part (b) to answer the following question: What is the probability
that a seat will be available for every person who shows up holding
a reservation? (Round your answer to four decimal places.)
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