Question

Suppose that an airline knows that there is a 95% chance that a passenger for a commuter flight that will hold 189 passengers will show up, and assumes that passengers arrive independently of one another. The airline decides to sell 199 tickets in order to reduce the number of empty seats, expecting 5% of the passengers not to show up.Let X be a random variable that represents the number of people who show up for the flight. Let Y = X –189 be a random variable representing the difference between the number of passengers who show up and the number of seats on the plane.a. Calculate E(X), Var(X), E(Y), and Var(Y).Justify your calculations by stating the type of distribution for X and Y. b.Calculate P(Y > 0). How do you feel about the airline’s decision to sell 199 tickets? c.The airline is conducting a review of their policies. They do not want the bad public relations that go along with having passengers with tickets not getting a seat. They have decided to hire you as a consultant to help give them advice. After some investigating, you have determined that as long as they have enough seats for passengers with tickets 98% of the time, they are willing to accept the risk.What is the largest value of n so that P(Y > 0) ≤0.02?

Answer 1