Question

Air-USA has a policy of booking as many as 24 persons on an airplane that can seat only 22. (Past studies have revealed that only 86% of the booked passengers actually arrive for the flight.) Find the probability that if Air-USA books 24 persons, not enough seats will be available. prob = Is this probability low enough so that overbooking problems will be unusual? (Define unusual as having probability 5% or less) yes, it is low enough no, it is not low enough What about defining unusual as 10% or less? no, it is not low enough yes, it is low enough

Answer 1

Answer:

The total probability is 13.15%

Step-by-step explanation:

Consider the provided information.

Air-USA has a policy of booking as many as 24 persons on an airplane that can seat only 22.

Studies have revealed that only 86% of the booked passengers actually arrive for the flight.

Therefore, the probability of a person arrive is 0.86

Find the probability that if Air-USA books 24 persons, not enough seats will be available.

That means either 23 person arrive or 24 person arrive.

Probability that 23 persons arrive = $^{24}C_{23}(0.86)^{23}(0.14)=0.1047$

Probability all 24 person arrive = $(0.86)^{24}=0.0268$

Total probability is: $0.1047+0.0268=0.1315$

Hence the total probability is 13.15%

So, in both cases its not low enough