13. Knowing that some passengers with tickets won't show up for a flight, airlines often "overbook" their flights by selling tickets to more passengers than a plane can accommodate. On a particular route, the plane holds 20 passengers and only 80% of ticket holders show up. For flights on this route, the airline sells 24 tickets for $400 each. If more than 20 ticket holders show up, the airline compensates the overbooked ticket holders with a voucher for $1000. Assume that ticket holders show up independently of each other and that al 24 tickets are sold. The table below shows part of the probability distribution of X= revenue (dollars) based on the number of ticket holders that show up. Number of ticket holders who show up X= revenue (dollars) P(X) 17 18 19 20 21 22 23 24 9600 9600 9600 9600 8600 7600 6600 5600 0.0998 0.1552 | 0.1960 | 0.1960 | 0.1493 0.0815 (a) Calculate the probability that exactly 23 of the ticket holders show up.

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13. Knowing that some passengers with tickets won't show up for a flight, airlines often "overbook" their
holders with a voucher for $1000. Assume that ticket holders show up independently of each other and that al
The table below shows part of the probability distribution of X= revenue (dollars) based on the number of
tickets for $400 each. If more than 20 ticket holders show up, the airline compensates the overbooked ticket
holds 20 passengers and only 80% of ticket holders show up. For flights on this route, the airline sells 24
flights by selling tickets to more passengers than a plane can accommodate. On a particular route, the plane
24 tickets are sold.
ticket holders that show up.
Number of ticket
holders who show up
17
18
19
20
21
22
23
24
onX= revenue (dollars)
P(X)
9600
9600
9600
9600
8600
7600
6600 5600
0.0998 | 0.1552 0.1960| 0.1960 | 0.1493 0.0815
(a) Calculate the probability that exactly 23 of the ticket holders show un
nottrvob innte bnu nom h o16 iemoglonrmizenggs ei zaml m ldsto no ta
(b) The expected revenue under these conditions is E(X) = $9184. Interpret this value.
(c) How much additional revenue does the airline expect to make by selling 24 tickets rather than 20?q
(d) Explain how you would determine the ideal number of tickets to sell if the goal is to maximize expected.
revenue.
र
Transcribed Image Text:13. Knowing that some passengers with tickets won't show up for a flight, airlines often "overbook" their holders with a voucher for $1000. Assume that ticket holders show up independently of each other and that al The table below shows part of the probability distribution of X= revenue (dollars) based on the number of tickets for $400 each. If more than 20 ticket holders show up, the airline compensates the overbooked ticket holds 20 passengers and only 80% of ticket holders show up. For flights on this route, the airline sells 24 flights by selling tickets to more passengers than a plane can accommodate. On a particular route, the plane 24 tickets are sold. ticket holders that show up. Number of ticket holders who show up 17 18 19 20 21 22 23 24 onX= revenue (dollars) P(X) 9600 9600 9600 9600 8600 7600 6600 5600 0.0998 | 0.1552 0.1960| 0.1960 | 0.1493 0.0815 (a) Calculate the probability that exactly 23 of the ticket holders show un nottrvob innte bnu nom h o16 iemoglonrmizenggs ei zaml m ldsto no ta (b) The expected revenue under these conditions is E(X) = $9184. Interpret this value. (c) How much additional revenue does the airline expect to make by selling 24 tickets rather than 20?q (d) Explain how you would determine the ideal number of tickets to sell if the goal is to maximize expected. revenue. र
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