Question

11. An airline estimates that 90% of people booked on their flights actually show up. If the airline books 82 people on a flight for which the maximum number is 78, what is the probability that the number of people who show up will exceed the capacity of the plane? (binomial probability)

Answer 1

We are given that 90% of the people booked on the airline's flights actually show up which means that the probability that a randomly selected person booked on the airline's flight actually shows up is equal to 90% = 0.9.

Now, let X denote the random variable representing the number of people who show up on the flight on which 82 people are booked.

Since, there is a fixed number of people booked on the flight (equal to 82), each person booked on the flight has two outcomes (showing up or not showing up) and each person booked on the flight shows up with probability 0.9 independent of other people booked on the flight, thus we can conclude that:

X ~ Binomial(n = 82, p = 0.9) and the probability mass function of X is given by:

Now, we are given that the capacity of the flight is 78 and we need to find the probability that the number of people who show up will exceed the capacity of the plane, i.e., we need to find the probability of the event 'X>78':

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