South Central Airlines (SCA) operates a commuter fight between Atlanta and Chari

Q: South Central Airlines (SCA) operates a commuter fight between Atlanta and Chari

Part a answer The table for calculation is given as below: Passengers showing up X Probability P(X) Cumulative Probability XP(X) 47 0.05 0.05 2.35 48 0.3 0.35 14.4 49 0.4 0.75 19.6 50 0.15 0.9 7.5 51 0.1 1 5.1 Total 1 Mean = 48.95 Average net profit = 48.95*100 = $4895 Average net profit = $4895 Part b answer Required probability = P(X

ID: 3155390 • Letter: S

Question

South Central Airlines (SCA) operates a commuter fight between Atlanta and Chariot to. the regional je holds 48 passengers and currently SCA only book up to 48 reservations. Past data show, that SCA always sells all 48 reservations, but on average, three passengers do not show up. As a result, with 48 reservations, the flight is often being flown with empty seats. To capture pro SCA is considering an overbooking stretch in which they would accept 51 reservations even though the airplane holds only 48 passengers. SCA beefcakes that it we be able to away book all SI reservations The probability Attribution for the number of passengers showing up when SI reservations arc accept cd is estimated as follows: SCA receive a marginal profit of $100 (or each passenger who books a reservation (regards whether they show up or not). The artery wall alto incur a cost for any passenger denied eating on the flight This cost covers added expenses Of rescheduling the passenger as well as lost erg goodwill, estimated to be $ 140 per passenger. Develop a spread sheet simulation model for this overbooking system Simulate the number of passengers showing up for a flight (Do 100 simulations). Assume the retinue from every ticket booked, even H the passenger doesn't show up. What it the average net pro for each fight with the overbooking strategy? If required, round your answer to the nearest dollar. What is the probability that the net profit with the overbooking strategy will be less than the net profit without overbooking (48*$100 = $4.800)? If required, round your answer to two decimal places.

Explanation / Answer

Part a answer

The table for calculation is given as below:

Passengers showing up X

Probability P(X)

Cumulative Probability

XP(X)

0.05

2.35

0.3

0.35

14.4

0.4

0.75

19.6

0.15

0.9

7.5

0.1

5.1

Total

Mean =

48.95

Average net profit =

48.95*100 = $4895

Average net profit = $4895

Part b answer

Required probability = P(X<48) = P(X=47) = 0.05