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

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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 [tex]\frac{88}{100}[/tex] = 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 [tex]^{354}C_n (0.88)^n (0.12)^{354 - n}[/tex].

The required probability is ∑[tex]^{354}C_n (0.88)^n (0.12)^{354 - n}[/tex], where [tex]331\leq n \leq 354[/tex].

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