Northwest Reginal Airlines (NWRA) operates a regional flight between Seattle and San Jose. The regional jet holds 80 passengers, and currently NWRA books only up to 80 reservations. Past data shows that NWRA sells all 80 reservations but usually not all the passengers show up to the flight. As a result, with 80 reservations, the flight is often being flown by empty seats. To capture additional profit, NWRA is considering an overbooking strategy in which they would accept 84 reservations even though the airplane holds 80 passengers. NWRA believes that it will be able to always book all 84 reservations. The probability distribution for the number of passengers showing up is uniform from 72 to 84 passengers. The average profit NWRA receives per passenger for each flight is around $120 but fluctuates based on additional charges such as extra luggage or pre-purchased in-flight food/beverage sales and can be represented with a normal distribution with mean $120 and standard deviation of $5. The airline will also incur a cost for any passenger denied seating on the flight. This cost, which covers the added expenses of rescheduling the passenger as well as loss of goodwill, is estimated to be $250 per passenger. Develop a spreadsheet simulation model for this overbooking system.

a. What is the average net profit for each flight with the overbooking strategy?

b. What is the probability that the net profit with the overbooking strategy will be greater than the net profit without overbooking?