(b) The expected revenue under these conditions is E(X) = $9184. Interpret this value. %3D

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number 13 b
flights by selling tickets to more passengers than a plane can accommodate. On a particular route, the plane
13. Knowing that some passengers with tickets won't show up for a flight, airlines often "overbook" their
holds 20 passengers and only 80% of ticket holders show up. For flights on this route, the airline sells 24
holders with a voucher for $1000. Assume that ticket holders show up independently of each other and that al
tickets for $400 each. If more than 20 ticket holders show up, the airline compensates the overbooked ticket
24 tickets are sold.
ticket holders that show up.
Number of ticket
holders who show up
17
18
19
20
21
22
23
24
9600
9600
0.0998 0.1552 | 0.1960 | 0.1960 | 0.1493 0.0815
9600
9600
E X= revenue (dollars)
P(X)
8600
7600
6600 5600
(a) Calculate the probability that exactly 23 of the ticket holders show up
(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?
(d) Explain how you would determine the ideal number of tickets to sell if the goal is to maximize expected
revenue.
wula Joord l leina) 1ot 2oml meat lo noiindreth orb lo nodso Inoste
Transcribed Image Text:flights by selling tickets to more passengers than a plane can accommodate. On a particular route, the plane 13. Knowing that some passengers with tickets won't show up for a flight, airlines often "overbook" their holds 20 passengers and only 80% of ticket holders show up. For flights on this route, the airline sells 24 holders with a voucher for $1000. Assume that ticket holders show up independently of each other and that al tickets for $400 each. If more than 20 ticket holders show up, the airline compensates the overbooked ticket 24 tickets are sold. ticket holders that show up. Number of ticket holders who show up 17 18 19 20 21 22 23 24 9600 9600 0.0998 0.1552 | 0.1960 | 0.1960 | 0.1493 0.0815 9600 9600 E X= revenue (dollars) P(X) 8600 7600 6600 5600 (a) Calculate the probability that exactly 23 of the ticket holders show up (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? (d) Explain how you would determine the ideal number of tickets to sell if the goal is to maximize expected revenue. wula Joord l leina) 1ot 2oml meat lo noiindreth orb lo nodso Inoste
Expert Solution
Step 1

(13 b )

X: revenue based on the no of people show up

E(X)=$9184

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