An airline estimates that 97 of people booked on their fligh

An airline estimates that 97% of people booked on their flights actually show up. If the airline books 70 people on a flight for which the maximum number is 68, what is the probability that the number of people who show up will exceed the capacity of the plane?

Solution

Binomial distribution,

n = 70, p = .97, q = .03

P[x] = nCx * p^x * q^(n-x), so

P[>68] = P[69] + P[70]
= 70C69 * 0.97^69 * 0.03 + 0.97^70
=0.3753 Answer