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.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![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
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(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.
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