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In: Statistics and Probability

When someone buys a ticket for an airline​ flight, there is a 0.0986 probability that the...

When someone buys a ticket for an airline​ flight, there is a 0.0986 probability that the person will not show up for the flight. A certain jet can seat 12 passengers. Is it wise to book 14 passengers for a flight on the​ jet? Explain Determine whether or not booking 14 passengers for 12 seats on the jet is a wise decision. Select the correct choice below and fill in the answer box in that choice with the probability that there are not enough seats on the jet.

A. It is not a wise decision because the probability that there are not enough seats on the jet is...........​So, overbooking is not an unlikely event.

B. It is a wise decision because the probability that there are not enough seats on the jet is............. ​So, overbooking is an unlikely event.

C. It is a wise decision because the probability that there are not enough seats on the jet is............ ​So, overbooking is not an unlikely event.

D. It is not a wise decision because the probability that there are not enough seats on the jet is.......... ​So, overbooking is an unlikely even

Solutions

Expert Solution

When someone buys a ticket for an airline​ flight, there is a 0.0986 probability that the person will not show up for the flight. This is same as

The probability that a person who buys a ticket will not show up for the flight is 0.0986

From this, we can get the probability that a person who buys a ticket will show up for the flight is 1-0.0986=0.9014

Let X be the number of passengers who show up out of 14 who bought a ticket. We can say that X has a Binomial distribution with parameters, number of trials (number of passengers booked) n=14, success probability (The probability that a person who buys a ticket will not show up for the flight) p=0.9014

The probability that X=x passengers show up is

the probability that there are not enough seats on the jet is same as the probability that more than 12 passengers turn up.

Any event with probability of 0.05 or less is is considered to be unlikely. The probability that there are not enough seats on the jet is 0.5918. Since this is greater than 0.05, we will consider the event of not having enough seats as "not unlikely"

ans: A. It is not a wise decision because the probability that there are not enough seats on the jet is >0.05 (or 0.5918). ​So, overbooking is not an unlikely event.

orchestra answered 2 years ago
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