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 154 passengers. If the airline believes the rate of passenger no-shows is 7% and sells 166 tickets, is it likely they will not have enough seats and someone will get bumped? a) Use the normal model to approximate the binomial to determine the probability of at least 155 passengers showing up. b) Should the airline change the number of tickets they sell for this flight? Explain. a) The probability of at least 155 passengers showing up is Round to three decimal places as needed) b) Should the airline change the number of tickets they sell for this flight? Explain O A. Since the proportion is so high, they should not change the number of tickets they sell O B. The proportion is fairly low, so it is likely that they should not change the number of tickets they sell. However, the decision also depends on the relative costs of not selling seats and bumping passengers O C. Since the proportion is so low, they should change the number of tickets they sell ( D. The proportion is very high, so it is likely that they should sell less. However, the decision also depends on the relative costs of not selling seats and bumping passengers

Answer 1

mean = 0.93*166 = 154.38
sd = sqrt(0.93*0.07*166) = 3.2873

P(X >= 155)
= P(z >= (155 - 154.38)/3.2873)
= P(z >= 0.1886)
= 0.4252

Option A