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.

Step-by-step explanation:

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

The probability of 1 passenger to come is $\frac{88}{100}$ = 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 $331\leq n \leq 354$.