Suppose that an airline knows that there is a 95% chance that apassenger for a commuter flight that will hold 189 passengers willshow up, and assumes that passengers arrive independently of oneanother. The airline decides to sell 199 tickets in order to reducethe number of empty seats, expecting 5% of the passengers not toshow up.Let X be a random variable that represents the number ofpeople who show up for the flight. Let Y = X –189 be a randomvariable representing the difference between the number ofpassengers who show up and the number of seats on the plane.a.Calculate E(X), Var(X), E(Y), and Var(Y).Justify your calculationsby 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 199tickets? c.The airline is conducting a review of their policies.They do not want the bad public relations that go along with havingpassengers with tickets not getting a seat. They have decided tohire you as a consultant to help give them advice. After someinvestigating, you have determined that as long as they have enoughseats for passengers with tickets 98% of the time, they are willingto accept the risk.What is the largest value of n so that P(Y >0) ≤0.02?
