Question 4 Airlines and hotels often grant reservations in excess of capacity to

Question

Question 4 Airlines and hotels often grant reservations in excess of capacity to minimize losses due to no- shows. Reservation agents must use diseretion, however, because the loss potential may be gleater when they cannot accommodate an alliving customer with a valid reservation (Consumer advocate Ralph Nader won a substantial sum in a class action suit after he was bumped hom a flight although he hadalid reservation.) An airline reservation office has found a) If the reservation office accepts 160 reservations for the flight and there are only 155 available seats on the plane, w hat is the probability that a seat will be available for every passenger who arrives with a valid reservation?

Explanation / Answer

This is a binomial distribution problem with probability of success, p = 0.05(passenger not arriving)

For seat to be available for all passengers, we require at least 5 people to not show up.

Let X represent the number of people not showing up.

Formula: P(X = k) = nck * pk * (1-p)(n-k)

P(X >= 5) = 1 - P(X < 5) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)
= 1 - 0.95160 - 160C1 * 0.05 * 0.95159 -160C2 * 0.052 * 0.95158 - 160C3 * 0.053 * 0.95157 - 160C4 * 0.054 * 0.95156
= 0.9061

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