Question

Airlines typically overbook flights. One airline knows the rate of people who actually take the flight is 92%. Flight 300 has 75 seats available, and the company sold 84 tickets. What is the probability they get 75 or fewer people on this flight?

(a) 0.031
(b) 0.073
(c) 0.999
(d) 0.927

Answer 1

The question deals with finding the probability of an overbooked flight having 75 or fewer passengers using the binomial probability or a normal approximation due to high ticket count and high probability of passengers showing up.

Step-by-step explanation:

The student's question about the probability that an airline will get 75 or fewer people on a flight with 75 seats available but selling 84 tickets can be addressed by using the binomial probability formula, considering each ticket sold has a 92% chance of resulting in an actual passenger. However, for a large number of tickets and a probability close to 1, it may be more appropriate to use a normal approximation to the binomial distribution. In this case, it's best to calculate the expected number of passengers and the standard deviation, then use the normal distribution to find the probability of 75 or fewer passengers showing up.