An airline estimates that 92% of people booked on their flights actually show up. if the airline books 75 people on a flight for which the maximum number is 73, what is the probability that the number of people who show up will exceed the capacity of the plane?

The probability is 0.0144

Step-by-step 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