Question

An airline estimates that 90% of people booked on their flight actually show up. If the airline books 71 people on a flight for which the maximum number is 69, what is the probability that the number for people who show up will exceed the capacity of the plane?

Answer 1

The probability is 0.0144

Explanation:

The probability that x people show up follows a binomial distribution, so it is equal to:

Where n is the number of booked people and p is the probability that a person shows up. Then, the probability that x people show up is:

So, the probability that the number of people who show up will exceed the capacity of the plane is:

P(x>73) = P(74) + P(75)

Where P(74) and P(75) are calculated as:

Finally, P(x>73) is:

P(x>73) = 0.0125 + 0.0019 = 0.0144