Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 161

Airline Flights: No-Shows Based on long experience, an airline has found that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline over-books 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. Which expression represents the probability that a seat will be available for everyone who shows up holding a reservation
P (255 r ); P ( r 255); P ( r 267); P ( r = 255)
(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