Exercise #3 (20pt): You're a systems engineer at Kash Air airlines charged with helping the airline to overbook flights. You realize that a certain percentage of ticketed passengers will cancel at the last minute. Therefore, to avoid empty seats, the airline wants to sell more tickets than there are seats, hoping that just about the right number of passengers show up. You assume that the no-show rate is 8% and assume that passengers choose to show up independently of each other. For a flight with 200 seats, the airline wants to see how sensitive various probabilities are to the number of tickets it issues. a. Calculate the probability that more than 205 passengers show up for the flight. b. Calculate the probability that more than 200 passengers show up. c. Calculate the probability that at least 195 passengers show up. d. Calculate the probability that at least 190 passengers show up. You're going to suggest that the airline issues a minimum of 205 tickets for the flight, and as many as 230, with all possibilities in between. Use Excel to calculate the four probabilities in a-d for each of the ticket allotment possibilities (be thoughtful in setting up the parameters so that you do as little manual entering as possible - this problem can be answered quickly with some thought on setting it up properly). Use the output of this exercise to make an informed decision about how many tickets to issue considering the risks of (1) operating a flight without maximizing revenue and (2) overselling. For this discussion, define the likelihood that flights will have exact capacity or fewer passengers (more than one options are possible) and the likelihood of overbooking the flight.