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Question 4. South Central Airlines operates a commuter flight between Atlanta and Charlotte. The plane holds 30 passengers, and the airline makes a $100 profit on each passenger on the flight. When South Central takes 30 reservations for the flight, experience has shown that, on average, two passengers do not show up As a result, with 30 reservations, South Central is averaging 28 passengers with a profit of per flight. The airline operations office has asked for an evaluation of an overbooking strategy in which the airline would accept 32 reservations even though the airplane holds only 30 passengers. The probability distribution for the number of passengers showing up when 32 reservations are accepted is as follows Passengers Showing Up 28 29 30 31 32 Probability 0.05 0.25 0.50 0.15 0.05 The airline will receive a profit of $100 for each passenger on the flight, up to the capacity of 30 passengers. The airline will also incur a cost for any passenger denied seating on the flight. This cost covers added expenses of rescheduling the passenger as well as loss of goodwill, estimated to be $150 per passenger a) Set up intervals of random numbers that can be used to simulate the number of new accounts opened at a seminar. (5 pts) b) Using the 10 random numbers below, simulate the number of passengers showing up for each of 10 flights. (5pts) 0.1642 0.2086 0.6078 0.5044 0.0484 0.4691 0.7058 0.8552 0.5029 0.3288 c) Based on the simulation of 10 flights from part b, compute the profit for each flight (10 pts)