Question

An airline company is considering a new policy of booking as many as 354 persons on an airplane that can seat only 330. (Past studies have revealed that only 88% of the booked passengers actually arrive for the flight.) Estimate the probability that if the company books 354 persons, not enough seats will be available

Answer 1

Title:

See the explanation.

Explanation:

It is given that, if 100 persons book their seats, then only 88 passengers come.

The probability of 1 passenger to come is
`(88)/(100)` = 0.88.

There will not be enough seats only when, 331 or more than 331 passengers will come.

The probability of 1 passenger will not come is (1 - 0.88)= 0.12.

Out of 354 passengers the probability that n passengers will come is
`^(354)C_n (0.88)^n (0.12)^(354 - n)`.

The required probability is ∑
`^(354)C_n (0.88)^n (0.12)^(354 - n)`, where
`331\leq n \leq 354`.