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Chapter5Quiz-MATH1123sectionOBFall2023_WebAssign.pdf
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
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MATH1123, section OB, Fall 2023
Chapter 5 Quiz (Quiz) INSTRUCTOR
Hua He
Hawaii Paci�c University
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SUN, NOV 19, 2023
11:59 PM HST
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11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=33177287 2/12
A bookstore sells books in several formats—hardcover, paperback, digital, and audio.
Based on past sales, the table below gives the estimated probabilities that a randomly selected purchase will be of particular types.
Hardcover Paperback Digital Audio
0.17 0.35 0.41 0.07
(a) If a purchase is selected at random, what is the probability that this purchase is for a book that is digital or audio?
.48
(b) If a purchase is selected at random, what is the probability that this purchase is for a book that is not digital?
.59
(c) If a purchase is selected at random, what is the probability that this purchase is for a book that is a printed book?
.52
The probability of getting a king when a card is selected at random from a standard deck of 52 playing cards is
(a) Give a relative frequency interpretation of this probability. (Enter your probability as a fraction.)
In the long run, 4/52 of all cards selected at random from a standard deck will be kings.
(b) Express the probability as a decimal rounded to three decimal places.
.077
Then complete the following statement. (Round your answer to the nearest integer.)
If a card is selected at random, I would expect to see a king about 77 times in 1,000.
. 1 13
1. [3/3 Points] PECKSTAT3 5.1.006.MI.DETAILS PREVIOUS ANSWERS MY NOTES
2. [3/3 Points] PECKSTAT3 5.1.008.DETAILS PREVIOUS ANSWERS MY NOTES
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
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A college job placement center has requests from five students for employment interviews. Three of these students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer has time to talk to only two of the students. These two will be randomly selected from among the five.
(a) What is the sample space for the chance experiment of selecting two students at random? (Hint: You can think of the students as being labeled A, B, C, D, and E. One possible selection of two students is A and B. There are nine other possible selections to consider.) (Enter your answers in the form AB. Enter your answers as a comma-separated list.)
$$AB,AC,AD,AE,BC,BD,BE,CD,CE,DE
(b) Are the outcomes in the sample space equally likely?
(c) What is the probability that both selected students are statistics majors?
1/10
(d) What is the probability that both students are math majors?
3/10
(e) What is the probability that at least one of the students selected is a statistics major?
7/10
(f) What is the probability that the selected students have different majors?
3/5
Yes
No
3. [6/6 Points] PECKSTAT3 5.2.014.DETAILS PREVIOUS ANSWERS MY NOTES
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=33177287 4/12
An article reported the following information for first-time freshmen at four-year colleges.
A total of 95,280 first-time freshmen were surveyed. 52,368 were enrolled in their first-choice college. 26,132 were enrolled at their second choice college. The rest were enrolled at a college that was not their first- or second-choice college.
(a) What is the probability that a randomly-selected person who participated in this survey was enrolled in their second-choice college? (Round your answer to four decimal places.)
.2743
(b) What is the probability that a randomly-selected person who participated in this survey was not enrolled at their first-choice college? (Round your answer to four decimal places.)
.4504
(c) What is the probability that a randomly-selected person who participated in this survey was not enrolled at either their first- or second-choice college? (Round your answer to four decimal places.)
.1766
4. [2/3 Points] PECKSTAT3 5.2.018.DETAILS PREVIOUS ANSWERS MY NOTES
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
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Each person in a representative sample of 3,337 students at two-year colleges was asked how they would describe their household's financial situation compared to before the COVID-19 pandemic. Each person in the sample was also asked if they have children who depend on them for care living with them. The responses are summarized in the table.
Better than Before Same as Before Worse than Before
Children 41 300 308
No Children 212 1,509 967
Suppose one of these 3,337 two-year college students is to be selected at random.
(a) What is the probability that the selected student has children? (Round your answer to four decimal places.)
.1945
(b) What is the probability that the selected student responded that they are better off than before the pandemic?
.0758
(c) What is the probability that the selected student has children and reported their financial situation was worse than before the pandemic?
.0923
(d) What is the probability that the selected student does not have children and reported that their financial situation was the same as before the pandemic?
.4522
(e) What is the probability that the selected student does not have children and reported their financial situation was worse than before the pandemic?
.2898
(f) Are the events and independent events? Use probabilities calculated from the information in the given table to justify your answer.
Since we see that the events C and W are not independent.
C = selected student has children W = selected student responded they are worse off
P C ∩ W ≠ P(C) + P(W)
5. [8/9 Points] PECKSTAT3 5.3.032.DETAILS PREVIOUS ANSWERS MY NOTES
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
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An appliance manufacturer offers extended warranties on its washers and dryers. Based on past sales, the manufacturer reports that of customers buying both a washer and a dryer, 42% purchase the extended warranty for the washer, 45% purchase the extended warranty for the dryer, and 57% purchase at least one of the two extended warranties.
(a) Use the given probability information to set up a hypothetical 1,000 table. (Let W be the event that the customer purchases an extended warranty for the washer. Let D be the event the customer purchases an extended warranty for the dryer.)
D Not D Total
W 570 450
Not W 450
Total 570 1,000
(b) Use the table from part (a) to find the following probabilities.
(i) the probability that a randomly selected customer who buys a washer and a dryer purchases an extended warranty for both the washer and the dryer
(ii) the probability that a randomly selected customer purchases an extended warranty for neither the washer nor the dryer
6. [0/10 Points] PECKSTAT3 5.3.034.MI.DETAILS PREVIOUS ANSWERS MY NOTES
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=33177287 7/12
A website provides data on the on-time performance of airlines. Suppose that the tables below summarize data from this website for flights that occurred over a 1 year time period.
(a) The following table summarizes data for flights leaving the Phoenix and Seattle airports for two airlines, Airline A and Airline B.
On-Time Departure Late Departure Total
Airline A 32,976 4,530 37,506
Airline B 46,762 6,536 53,298
Total 79,738 11,066 90,804
Suppose that one of these flights is selected at random.
(i) What is the probability that the flight had an on-time departure? (Round your answer to four decimal places.)
.8781
(ii) What is the probability that the flight had an on-time departure given that it was an Airline A flight? (Round your answer to four decimal places.)
.3631
(iii) What is the probability that the flight had an on-time departure given that it was an Airline B flight? (Round your answer to four decimal places.)
.5150
(iv) Which airline had the better on-time performance?
(b) Now consider the flight data for just the Phoenix airport.
On-Time Departure Late Departure Total
Airline A 29,382 3,777 33,159
Airline B 2,774 319 3,093
Total 32,156 4,096 36,252
Suppose that one of these flights from the Phoenix airport is selected at random.
(i) What is the probability that the flight had an on-time departure? (Round your answer to four decimal places.)
.8870
(ii) What is the probability that the flight had an on-time departure given that it was an Airline A flight? (Round your answer to four decimal places.)
Airline A
Airline B
7. [9/18 Points] PECKSTAT3 5.4.052.DETAILS PREVIOUS ANSWERS MY NOTES
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
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.8105
(iii) What is the probability that the flight had an on-time departure given that it was an Airline B flight? (Round your answer to four decimal places.)
.0765
(iv) Which airline had the better on-time performance?
(c) Now consider the flight data for just the Seattle airport.
On-Time Departure Late Departure Total
Airline A 3,594 753 4,347
Airline B 43,988 6,217 50,205
Total 47,582 6,970 54,552
Suppose that one of these flights from the Seattle airport is selected at random.
(i) What is the probability that the flight had an on-time departure? (Round your answer to four decimal places.)
.8722
(ii) What is the probability that the flight had an on-time departure given that it was an Airline A flight? (Round your answer to four decimal places.)
(iii) What is the probability that the flight had an on-time departure given that it was an Airline B flight? (Round your answer to four decimal places.)
.8063
(iv) Which airline had the better on-time performance? (Round your answer to four decimal places.)
(d) You should have noticed from parts (b) and (c) that for both the Phoenix airport and the Seattle airport, Airline B had the better on-time performance. But in part (a) when the data for both airports is combined, it looks like Airline A has slightly better on-time performance. This is an example of what is known as Simpson's Paradox. Write a brief explanation of why the apparent inconsistency occurs for this data set. (Hint: Does it look like the airports differ with respect to flight delays? Enter your numerical values as percents rounded to the nearest whole number.)
First, note that there were many more Airline B flights than Airline A flights overall. Second, note also that Airline B
flights had many more on-time departures than Airline A. With the combined data for both airports, %
of the flights were Airline A and % of the flights were Airline B. However, when one looks at the individual airports, there are much larger differences between the percent of flights for each airline. Although Airline B had a
Airline A
Airline B
Airline A
Airline B
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
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better on-time departure rate at both airports, when combined together, the differences between the flight percents is increased, deflating the Airline A on-time departure rate relative to Airline B.
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=33177287 10/12
A paper described the results of a medical study in which one treatment was shown to be better for men and better for women than a competing treatment. However, if the data for men and women are combined, it appears as though the competing treatment is better.
To see how this can happen, consider the accompanying data tables constructed from information in the paper. Subjects in the study were given either Treatment A or Treatment B, and their survival was noted. Let S be the event that a patient selected at random survives, A be the event that a patient selected at random received Treatment A, and B be the event that a patient selected at random received Treatment B. (Round your answers to three decimal places.)
(a) The following table summarizes data for men and women combined.
Survived Died Total
Treatment A 216 84 300
Treatment B 241 59 300
Total 457 143
(i) Find
(ii) Find
(iii) Find
(iv) Which treatment appears to be better?
(b) Now consider the summary data for the men who participated in the study.
Survived Died Total
Treatment A 120 80 200
Treatment B 20 20 40
Total 140 100
(i) Find
(ii) Find
P(S).
P(S|A).
P(S|B).
Treatment A
Treatment B
P(S).
P(S|A).
8. [4/13 Points] PECKSTAT3 5.4.501.XP.DETAILS PREVIOUS ANSWERS MY NOTES
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
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(iii) Find
(iv) Which treatment appears to be better?
(c) Now consider the summary data for the women who participated in the study.
Survived Died Total
Treatment A 96 4 100
Treatment B 221 39 260
Total 317 43
(i) Find
(ii) Find
(iii) Find
(iv) Which treatment appears to be better?
(d) You should have noticed from parts (b) and (c) that for both men and women, Treatment A appears to be better. But in part (a), when the data for men and women are combined, it looks like Treatment B is better. This is an example of what is called Simpson's paradox. Write a brief explanation of why this apparent inconsistency occurs for this data set. (Hint: Do men and women respond similarly to the two treatments?)
P(S|B).
Treatment A
Treatment B
P(S).
P(S|A).
P(S|B).
Treatment A
Treatment B
The results are distorted in favor of Treatment B, as women respond to these treatments better than men, but Treatment A was given to far more women than men.
The results are distorted in favor of Treatment B, as women respond to both treatments better than men, but Treatment B was given to far more women than men.
The results are distorted in favor of Treatment A, as women respond to both treatments better than men, but Treatment A was given to far more women than men.
The results are distorted in favor of Treatment A, as women respond to these treatments better than men, but Treatment B was given to far more women than men.
11/17/23, 10:29 PM Chapter 5 Quiz - MATH1123, section OB, Fall 2023 | WebAssign
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