Question

Because many passengers who make reservations do not show​ up, airlines often overbook flights​ (sell more tickets than there are​ seats). A certain airplane holds 296 passengers. If the airline believes the rate of passenger​ no-shows is 5​% and sells 308 ​tickets, is it likely they will not have enough seats and someone will get​ bumped?
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Use the normal model to approximate the binomial to determine the probability of at least 297 passengers showing up.
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Should the airline change the number of tickets they sell for this​ flight? Explain.
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The probability of at least 297 passengers showing up is
nothing.
​(Round to three decimal places as​ needed.)
​b) Should the airline change the number of tickets they sell for this​ flight? Explain.
A.
The proportion is fairly high​, so it is likely that they should sell less. ​However, the decision also depends on the relative costs of not selling seats and bumping passengers.
B.
Since the proportion is so low​, they should change the number of tickets they sell.
C.
Since the proportion is so high​, they should not change the number of tickets they sell.
D.
The proportion is fairly low​, so it is likely that they should not change the number of tickets they sell. ​However, the decision also depends on the relative costs of not selling seats and bumping passengers.

Answer 1

This is an example of binomial distribution

the airline believes the probability of passenger​ no-shows is 0.05

airplane capacity is 296. If more than 296people show someone will get bumped.

the airline sold 308 tickets

The probability that someone will be bumped( if 11 or fewer people do not show up) is ( use excel formula BINOM.DIST(11,308,0.05,TRUE))

The probability of at least 297 passengers showing up is 0.1530

b) the probability is greater than 15%. Hence it likely they will not have enough seats and someone will get​ bumped.

option A is right