An airline offers "advance-purchase" fares to customers who buy their tickets at least four weeks before the flight. The airline has noticed that 80% of its customers who buy tickets don't take advantage of advance-purchase fares and the remaining 20% do. The no-show rate for those who don't have advance-purchase fares is 25%, while for those who do have them, it is only 15%. (a) Calculate the probabilities labeled on the tree diagram below. (Give answers correct to three decimal places.) A tree diagram with 6 branches is shown. The tree diagram begins at a point and an upper and lower branch extend from this point to the right. From each of these two branches two more upper and lower branches extend to the right. The branches extending from the first point from top to bottom are labeled a and b and end at points labeled "no advance purchase" and "advance purchase" respectively. The branches extending from "no advance purchase" and "advance purchase" from top to bottom are labeled c, d, e, h and end at points labeled "no show", "show up", "no show", and "show up" respectively. A column to the right of the tree diagram labeled "Final probability" shows a value next to each of the four branches extending from "no advance purchase" and "advance purchase". From top to bottom, they are p, n, k and u. (b) Create a "hypothetical hundred thousand" table for this situation. Method Shows No Shows Total Buy Advance Tickets Doesn't Buy Advance Tickets Total (c) Using the tree diagram from part (a) or the table from part (b), find the percent of customers who are no-shows. %

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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An airline offers "advance-purchase" fares to customers who buy their tickets at least four weeks before the flight. The airline has noticed that 80% of its customers who buy tickets don't take advantage of advance-purchase fares and the remaining 20% do. The no-show rate for those who don't have advance-purchase fares is 25%, while for those who do have them, it is only 15%.

(a)

Calculate the probabilities labeled on the tree diagram below. (Give answers correct to three decimal places.)

A tree diagram with 6 branches is shown.

The tree diagram begins at a point and an upper and lower branch extend from this point to the right. From each of these two branches two more upper and lower branches extend to the right.
The branches extending from the first point from top to bottom are labeled a and b and end at points labeled "no advance purchase" and "advance purchase" respectively.
The branches extending from "no advance purchase" and "advance purchase" from top to bottom are labeled c, d, e, h and end at points labeled "no show", "show up", "no show", and "show up" respectively.
A column to the right of the tree diagram labeled "Final probability" shows a value next to each of the four branches extending from "no advance purchase" and "advance purchase". From top to bottom, they are p, n, k and u.

(b)

Create a "hypothetical hundred thousand" table for this situation.

Method	Shows	No Shows	Total
Buy Advance Tickets
Doesn't Buy Advance Tickets
Total

(c)

Using the tree diagram from part (a) or the table from part (b), find the percent of customers who are no-shows.

(d)

Given that a customer is a no-show, what is the probability that they had an advance-purchase fare? (Enter your answer as a fraction.)

(e)

Refer to the answer you found in part (d). Write a sentence presenting this result that someone with no training in statistics would understand.

About 13% of customers who do not show for this route had purchased advanced tickets.About 87% of customers who do not show for this route had purchased advanced tickets. About 87% of customers who show for this route had purchased advanced tickets.About 23% of customers who do not show for this route had purchased advanced tickets.About 13% of customers who show for this route had purchased advanced tickets.

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