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?

Bold a right parenthesis font size decreased by 1

Use the normal model to approximate the binomial to determine the
probability of at least 297 passengers showing up.

Bold b right parenthesis font size decreased by 1

Should the airline change the number of tickets they sell for this
flight? Explain.

Bold a right parenthesis font size decreased by 1

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

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