irlines routinely overbook flights based on the expectation that some fraction of booked passengerswill not show up for each flight. For a p
irlines routinely overbook flights based on the expectation that some fraction of booked passengerswill not show up for each flight. For a particular flight, there are only 50 seats, but the airline has sold52 tickets. Assume that a booked passenger will not show for the flight with probability 5%.
[2 points] Let X be the number of passengers that arrive for the flight. Under what assump- tion(s) is X a Binomial random variable?
[2 points] For the remaining questions, we will assume X is Binomial. What are the values of the relevant parameters?
[3 points]Using the Binomial frequency function, find the exact probability that 51 passengers arrive. Also find the exact probability that 52 passengers arrive.
[1 points] What is the probability that there will not be enough seats on the plane?
[5 points] If there are not enough seats, then the airline has to pay a penalty of 500$ to each passenger who cannot ride. In other words, the total penalty is 500$ if 51 passengers arrive and 1000$ if 52 passengers arrive. Find the expected value and the variance of the amount the airline will have to pay.