Question

American Air Flight 2705 from New York to San Francisco has seats for 340 passengers. An average of 5% if people with reservations don’t show up, so American Air overbooks by accepting 350 reservations for the 340 seats. We can analyze this system by using a binomial distribution with n = 350 and p = 0.95 (the probability that someone with a reservation does not show up). Find the probability that when 350 reservations are accepted for a particular flight, there are more passengers than seats. That is, find the probability of at lest 341 people showing up with reservation, assuming that 350 reservations were accepted.

Answer 1

Let X be the number of with reservations show up

X follows Binomial(n = 350, p = 0.95)

The probability that when 350 reservations are accepted for a particular flight, there are more passengers than seats would be

P(X ≥ 341) = 1 - P(X ≤ 340)

We can use Binomial probabilities using =BINOM.DIST(number_s, trials, probability_s, cumulative) excel function. For P(X ≤ 340), =BINOM.DIST(340, 350, 0.95, TRUE) (cumulative TRUE since it is ≤)

P(X ≥ 341) = 1 - 0.982120005 = 0.017879995