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 tícket holders with a voucher for $1000. Assume that ticket holders show up independently of each other and that al 24 tickets are sold. t of the probability distribution of X= revenue (dol
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 tícket holders with a voucher for $1000. Assume that ticket holders show up independently of each other and that al 24 tickets are sold. t of the probability distribution of X= revenue (dol
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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number 13 c
Transcribed Image Text:13. Knowing that some passengers with tickets won't show up for a flight, airlines often "overbook" their
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
The table below shows part of the probability distribution of X= revenue (dollars) based on the number of
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
24 tickets are sold.
ticket holders that show up.
Number of ticket
holders who show up
LX= 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.
(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.
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