Question

An airline company is considering a new policy of booking as many as 191 persons on an airplane that can seat only 180. (Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.) Estimate the probability that if the company books 191 persons. not enough seats will be available.

Answer 1

1.3559644*10^-^5

Explanation:

From the information given we extract the following data

Total Number of Trials (N) = 191

Required Value (x) = 181 (notice it is not 180 since at that value we have enough passengers)

Odds of success (p) = 0.85

Using the binomial formula for calculating probability, i.e.

`P(x; N, p) = nCx * p^x *(1-p)^(N-x)`

Inputting the values

`P(181; 191, 0.85) = 191C181 *0.85^(181)  *(1-0.85)^(191-181) \\ P(181; 191, 0.85) = 1.3559644*10^-^5`