Question

A common practice of airline companies is to sell more tickets for a particular flight than there are seats on the plane, because customers who buy tickets do not always show up for the flight. suppose that the percentage of no shows at flight time is 3%. For a particular flight with 298 seats a total of 310 tickets were sold. What is the probability that the airline overbooked this flight?

Answer 1

The probability that the airline overbooked this flight is approximately 0.996 or 99.6%.

Step-by-step explanation:

To calculate the probability that the airline overbooked the flight, we need to determine the probability of more customers showing up than there are seats available. In this case, 310 tickets were sold for a flight with 298 seats. The percentage of no-shows is 3%, which means the probability of a customer not showing up is 0.03.

We can use the binomial probability formula to calculate the probability. Let X be the number of customers showing up:

P(X > 298) = 1 - P(X <= 298)

P(X <= 298) = (1 - 0.03)^310

≈ 0.004

P(X > 298) = 1 - 0.004

≈ 0.996

Therefore, the probability that the airline overbooked this flight is approximately 0.996 or 99.6%.