Question

An airline estimates that 94% of people booked on their flights actually show up. If the airline books 80 people on a flight for which the maximum number is 77, what is the probability that the number of people who show up will exceed the capacity of the plane?

Answer 1

To find the probability that the number of people who show up exceeds the capacity of the plane, we need to find the probability that more than 77 people show up. We can use the binomial probability formula to calculate this probability.

Step-by-step explanation:

To find the probability that the number of people who show up exceeds the capacity of the plane, we need to find the probability that more than 77 people show up. We know that 94% of people booked on the flights actually show up, so the probability that a booked person does not show up is 1 - 0.94 = 0.06.

Since the number of people who show up follows a binomial distribution with n = 80 (the number of people booked) and p = 0.06 (the probability that a booked person does not show up), we can use the binomial probability formula to calculate the probability of exceeding the capacity.

The probability can be calculated as follows:

P(X > 77) = P(X = 78) + P(X = 79) + P(X = 80)

where X is the number of people who show up.

Using the binomial probability formula, we can calculate each individual probability and sum them up to find the final answer.