Business Statistics A First Course 2nd Edition Sharpe Test Bank

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Chapter 7: Randomness and Probability – Quiz A Name

1. During its grand opening week, Stickler’s bicycle shop offers a “wheel of discount savings.” After customers select the items they wish to purchase, they spin the wheel to determine the discount they will receive. The wheel is divided into 12 slices. Six slices are red and award a 10% discount, three slices are white and award a 20% discount, and two slices are blue and award a 40% discount. The remaining slice is gold and awards a 100% discount!

a. What is the probability that a customer gets at least a 40% discount?

b. What is the probability that a customer does not get at least a 40% discount?

c. What is the probability that a customer gets a 10% or 20% discount?

d. What is the probability that two customers in a row get a 20% discount?

2. Suppose you visit Stickler’s bicycle shop in the hopes of getting a 100% discount on your purchases. As you wait your turn in line, there are three gold winners in a row. The two customers in line behind you begin to discuss what’s happened. One believes that the streak of three gold winners has killed anyone else’s chances of getting a 100% discount, while the other says just the opposite… that the wheel’s “hot streak” increases their chances of getting a 100% discount. Comment on these opinions.

3. A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both.

a. What is the probability that a cell phone sold last month had a camera or a music player?

b. What is the probability that a cell phone sold last month did not have either a camera or a music player?

c. Is a cell phone having a camera and a music player mutually exclusive? Explain.

4. A small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data.

a. What is the probability that an employee chose online training?

b. What is the probability that an employee is in the quality division and chose online training?

c. What is the probability that an employee chose online training given that he/she is in the sales division?

5. Does it appear that choice of instructional method (traditional or online) and division (sales, quality and operations) are independent? Explain.

6. One explanation put forth for the dearth of women CEO’s in the high tech industry is that there are a lack of mentoring opportunities for women. A recent survey of CEO’s in that industry found that 80% were men. Moreover, 75% had been mentored while only 15% were women and had been mentored.

a. Construct the contingency table.

b. Are gender and mentoring independent? Explain.

Business Statistics: Chapter 7: Randomness and Probability – Quiz A – Key

.25 (3/12) b. What is the probability that a customer does not get at least a 40% discount?

.75 (1-.25) complement rule c. What is the probability that a customer gets a 10% or 20% discount?

.75 (6/12 + 3/12 = 9/12) addition rule with mutually exclusive events d. What is the probability that two customers in a row get a 20% discount?

.0625 (3/12 x 3/12) independence rule a. What is the probability that a cell phone sold last month had a camera or a music player?

The spins are independent, so if the wheel is fair the three gold winners in a row have no effect on the next persons’ chances.

3. A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both.

.70 (.64 + .28 - .22) general addition rule b. What is the probability that a cell phone sold last month did not have either a camera or a music player?

.30 (1 - .70) complement rule c. Is a cell phone having a camera and a music player mutually exclusive? Explain. a. What is the probability that an employee chose online training?

No. The intersection of these two events is not zero.

.75 (102/136) b. What is the probability that an employee is in the quality division and chose online training?

.17 (23/136) c. What is the probability that an employee chose online training given that he/she is in the sales division?

.69 (35/51) a. Construct the contingency table. b. Are gender and mentoring independent? Explain.

5. Does it appear that choice of instructional method (traditional or online) and division (sales, quality and operations) are independent? Explain.

Since the marginal probability of choosing online training (.75) does not equal the conditional probability of choosing online training given the employee is in the sales division (.69), the choice of instructional method is not independent of division.

The conditional probability P(Mentored/Men) = .60/.80 = .75 which equals the marginal probability P(Mentored) = .75. Yes, mentoring is independent of gender.

Chapter 7: Randomness and Probability – Quiz B Name

1. As an incentive to get new customers, the local branch of a bank launched “bouncing for bucks.” During this week long event, any customer opening a new checking account with the bank would have the opportunity to throw a bouncy rubber ball into a large box divided into squares. Each square was labeled with a dollar amount that would be deposited into his/her new checking account. The way the box was labeled is shown below.

10 30 10 30 10 20 10 50 10 20 a. What is the probability that a customer gets $20 or more? b. What is the probability that a customer gets less than $20? c. What is the probability that a customer gets $20 or $30? d. What is the probability that two customers in a row get $50? a. What is the probability that in the last year a passenger redeemed frequent flyer miles to purchase a ticket for domestic or international travel? b. What is the probability that in the last year a passenger did not redeem frequent flyer miles to purchase a ticket for domestic or international travel? c. Is redeeming frequent flyer miles to purchase a ticket for domestic and international travel mutually exclusive? Explain. a. What is the probability that a consumer purchases an extended warranty? b. What is the probability that a consumer purchases a digital camera and an extended warranty? c. What is the probability that a consumer purchases an extended warranty given that he/she has purchased a digital camera? a. Construct the contingency table. b. Are gender and participation in online auctions independent? Explain.

2. As you enter the bank, you watch four persons in front of you all win $50. The local branch manager tells you how lucky you are to be throwing the ball while it is on a hot streak but the friend with you says that you’re unlucky because the streak can’t continue. Comment on their statements.

3. A major airline keeps track of data on how their passengers redeem frequent flyer miles. They found that in the last year 58% of passengers redeemed them to purchase tickets for domestic travel, 44% redeemed them to purchase tickets for international travel, and that 16% redeemed them to purchase tickets for both domestic and international travel.

4. The option to buy extended warranties is commonplace with most electronics purchases. But does the type of purchase affect a consumer’s willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table.

5. Does it appear that the decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are independent? Explain.

6. It has been reported that men are more likely than women to participate in online auctions. A recent study found that 52% of Internet shoppers are women and that 35% of Internet shoppers have participated in online auctions. Moreover, 25% of online shoppers were men and had participated in online auctions.

Chapter 7: Randomness and Probability – Quiz B – Key

10 30 10 30 10

20 10 50 10 20 a. What is the probability that a customer gets $20 or more?

.50 (5/10) b. What is the probability that a customer gets less than $20?

.50 (1 - .50) complement rule c. What is the probability that a customer gets $20 or $30?

.40 (2/10 + 2/10) addition rule with mutually exclusive events d. What is the probability that two customers in a row get $50?

.01 (1/10 x 1/10) independence rule a. What is the probability that in the last year a passenger redeemed frequent flyer miles to purchase a ticket for domestic or international travel?

The tosses are independent. So if the box and ball are fair, the four winners of $50 have no effect on the next person’s chances of winning $50.

.86 (.58 + .44 - .16) general addition rule b. What is the probability that in the last year a passenger did not redeem frequent flyer miles to purchase a ticket for domestic or international travel?

.14 (1 - .86) complement rule c. Is redeeming frequent flyer miles to purchase a ticket for domestic and international travel mutually exclusive? Explain. No, the intersection of these two events is not zero. a. What is the probability that a consumer purchases an extended warranty?

.42 (175/420) b. What is the probability that a consumer purchases a digital camera and an extended warranty?

.07 (30/420) c. What is the probability that a consumer purchases an extended warranty given that he/she has purchased a digital camera?

.42 (30/72)

5. Does it appear that the decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are independent? Explain.

Since the marginal probability of purchasing an extended warranty (..42) does equal the conditional probability of purchasing an extended warranty given the employee purchased a digital camera (.42), the decision to purchase an extended warranty is independent of type of electronics (digital camera or laptop computer) purchased.

6. It has been reported that men are more likely than women to participate in online auctions. A recent study found that 52% of Internet shoppers are women and that 35% of a. Construct the contingency table. b. Are gender and participation in online auctions independent? Explain.

Internet shoppers have participated in online auctions. Moreover, 25% of online shoppers were men and had participated in online auctions.

The conditional probability P(Yes Participated in Online Auction/Men) = .25/.48 = .52 does not equals the marginal probability P(Yes Participated in Online Auction) = .35. No, participation in online auctions is not independent of gender.

Chapter 7: Randomness and Probability – Quiz C Name

7.1. Use the basic rules and definitions of probability.

A. 3/12

B. 2/12

C. .0625

D. 9/12

E. 10/12

7.1. Use the basic rules and definitions of probability.

2. During its grand opening week, Stickler’s bicycle shop offers a “wheel of discount savings.” After customers select the items they wish to purchase, they spin the wheel to determine the discount they will receive. The wheel is divided into 12 slices. Six slices are red and award a 10% discount, three slices are white and award a 20% discount, and two slices are blue and award a 40% discount. The remaining slice is gold and awards a 100% discount! The probability that a customer gets a 10% or 20% discount is

A. 3/12

B. 2/12

C. .0625

D. 9/12

E. 10/12

7.3. Know the addition and multiplication rules for probability and how to apply them.

3. During its grand opening week, Stickler’s bicycle shop offers a “wheel of discount savings.” After customers select the items they wish to purchase, they spin the wheel to determine the discount they will receive. The wheel is divided into 12 slices. Six slices are red and award a 10% discount, three slices are white and award a 20% discount, and two slices are blue and award a 40% discount. The remaining slice is gold and awards a 100% discount! The probability that two customers in a row get a 20% discount is

A. 3/12

B. 2/12

C. .0625

D. 9/12

E. 10/12

7.3. Know the addition and multiplication rules for probability and how to apply them.

4. A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both. The probability that a cell phone sold last month had a camera or a music player is

A. .22

B. .70

C. .92

D. .30

E. .08

7.3. Know the addition and multiplication rules for probability and how to apply them.

5. A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both. The probability that a cell phone sold last month did not have either a camera or a music player is

A. .22

B. .70

C. .92

D. .30

E. .08

7.5. Determine if two events are disjoint or independent.

6. A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both. Which of the following statements about cell phones sold last month is true?

A. Having a camera and having a music player are mutually exclusive events.

B. The intersection of having a camera and having a music player is zero.

C. Having a camera and having a music player are independent events.

D. Having a camera and having a music player are disjoint events.

E. Having a camera and having a music player are not mutually exclusive events.

7.4. Use a contingency table.

7. The option to buy extended warranties is commonplace with most electronics purchases. But does the type of purchase affect a consumer’s willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table. The probability that a consumer does not purchase an extended warranty is

7.4. Use a contingency table.

8. The option to buy extended warranties is commonplace with most electronics purchases. But does the type of purchase affect a consumer’s willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table. The probability that a consumer purchases a digital camera and an extended warranty is

7.7. Use conditional probability.

9. The option to buy extended warranties is commonplace with most electronics purchases. But does the type of purchase affect a consumer’s willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table. The probability that a consumer purchases an extended warranty given that he/she has purchased a digital camera is

7.5. Determine if two events are disjoint or independent.

10. The option to buy extended warranties is commonplace with most electronics purchases. But does the type of purchase affect a consumer’s willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table. Which of the following statement is true?

A. The decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are independent.

B. The decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are mutually exclusive.

C. The decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are disjoint events.

D. The decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are not independent.

E. The decision to purchase an extended warranty and type of electronics (digital camera or laptop computer) purchased are related

7.7. Know how to use Bayes’ Rule to compute conditional probabilities.

11. As accounts manager in your company, you classify 75% of your customers as "good credit" and the rest as "risky credit" depending on their credit rating. Customers in the "risky" category allow their accounts to go overdue 50% of the time on average, whereas those in the "good" category allow their accounts to become overdue only 10% of the time. What percentage of overdue accounts are held by customers in the "risky credit" category? A. 20% B. 12.5% C. 93.75% D. 62.5%

Chapter 7: Randomness and Probability – Quiz C – Key

Business Statistics: Chapter 7: Randomness and Probability – Quiz D Name

7.1. Use the basic rules and definitions of probability.

10 30 10 30 10 20 10 50 10 20

7.1. Use the basic rules and definitions of probability.

2. As an incentive to get new customers, the local branch of a bank launched “bouncing for bucks.” During this week long event, any customer opening a new checking account with the bank would have the opportunity to throw a bouncy rubber ball into a large box divided into squares. Each square was labeled with a dollar amount that would be deposited into his/her new checking account. The way the box was labeled is shown below. What is the probability that a customer does not get $50?

10 30 10 30 10 20 10 50 10 20

7.3. Know the addition and multiplication rules for probability and how to apply them.

3. As an incentive to get new customers, the local branch of a bank launched “bouncing for bucks.” During this week long event, any customer opening a new checking account with the bank would have the opportunity to throw a bouncy rubber ball into a large box divided into squares. Each square was labeled with a dollar amount that would be deposited into his/her new checking account. The way the box was labeled is shown below. What is the probability that three customers in a row do not get $50?

10 30 10 30 10 20 10 50 10 20

A. 0.125

B. 0.001

C. 0.729

D. 0.970

E. 0.300

7.3. Know the addition and multiplication rules for probability and how to apply them.

4. As an incentive to get new customers, the local branch of a bank launched “bouncing for bucks.” During this week long event, any customer opening a new checking account with the bank would have the opportunity to throw a bouncy rubber ball into a large box divided into squares. Each square was labeled with a dollar amount that would be deposited into his/her new checking account. The way the box was labeled is shown below. Out of the next three customers that come into the bank and play the game, what is the probability that at least one gets $50?

10 30 10 30 10 20 10 50 10 20

A. 0.001

B. 0.271

C. 0.729

D. 0.300

E. 0.125

7.5. Determine if two events are disjoint or independent.

5. It has been reported that men are more likely than women to participate in online auctions. In a recent survey, 65% of respondents reported that they had participated in an online auction. In this same survey, 45% of respondents were men and 38% were men who had participated in online auctions. Which of the following is true?

A. Gender and participation in online auctions are independent.

B. Gender and participation in online auctions are disjoint.

C. The intersection of being male and participating in online auctions is zero.

D. Gender and participation in online auctions are not related.

E. Gender and participation in online auctions are dependent.

7.3. Know the addition and multiplication rules for probability and how to apply them.

6. It has been reported that men are more likely than women to participate in online auctions. In a recent survey, 65% of respondents reported that they had participated in an online auction. In this same survey, 45% of respondents were men and 38% were men who had participated in online auctions. What is the probability that a respondent selected at random is female and has never participated in an online auction?

A. 0.62

B. 0.72

C. 0.38

D. 0.28

E. 0.07

7.6. Use conditional probability.

7. It has been reported that men are more likely than women to participate in online auctions. In a recent survey, 65% of respondents reported that they had participated in an online auction. In this same survey, 45% of respondents were men and 38% were men who had participated in online auctions. What is the probability that a respondent had participated in an online auction given that he is male?

A. 0.38

B. 0.84

C. 0.62

D. 0.45

E. 0.55

7.1. Use the basic rules and definitions of probability. .

8. Suncast Cable offers high definition (HD) cable TV, Internet and phone services to its customers. For those service issues that can be resolved by calling its technical support center, Suncast’s goal is to have the problem solved within 30 minutes. In order to determine how well it is achieving this goal, they monitored calls to its technical support center over the last three months. The data compiled is shown in the table below. If Suncast wished to determine probabilities using these data, what type of probability would it be calculating?

7.4. Use a contingency table.

9. Suncast Cable offers high definition (HD) cable TV, Internet and phone services to its customers. For those service issues that can be resolved by calling its technical support center, Suncast’s goal is to have the problem solved within 30 minutes. In order to determine how well it is achieving this goal, they monitored calls to its technical support center over the last three months. The data compiled is shown in the table below. What is the probability that a call to the technical support center involved an issue with Internet service?

7.4. Use a contingency table.

10. Suncast Cable offers high definition (HD) cable TV, Internet and phone services to its customers. For those service issues that can be resolved by calling its technical support center, Suncast’s goal is to have the problem solved within 30 minutes. In order to determine how well it is achieving this goal, they monitored calls to its technical support center over the last three months. The data compiled is shown in the table below. What is the probability that a call to the technical support center involved an issue with Internet service or was not resolved within 30 minutes?

7.6. Know how to compute conditional probabilities and construct a probability tree.

11. A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time. Further, 15% of all steroid-free individuals also test positive. 10% of the rugby team members use steroids. Your friend on the rugby team has just tested positive. The correct probability tree looks like

7.7. Know how to use Bayes’ Rule to compute conditional probabilities.

12. A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time. Further, 15% of all steroid-free individuals also test positive. 10% of the rugby team members use steroids. Your friend on the rugby team has just tested positive. The probability that he uses steroids is A. 0.4130 B. 0.8636 C. 0.0950 D. 0.2300

Chapter 7: Randomness and Probability – Quiz A Name

Business Statistics: Chapter 7: Randomness and Probability – Quiz A – Key

Chapter 7: Randomness and Probability – Quiz B Name

Chapter 7: Randomness and Probability – Quiz B – Key

Chapter 7: Randomness and Probability – Quiz C Name

Chapter 7: Randomness and Probability – Quiz C – Key

Business Statistics: Chapter 7: Randomness and Probability – Quiz D Name

7.6. Know how to compute conditional probabilities and construct a probability tree.

7.7. Know how to use Bayes’ Rule to compute conditional probabilities.

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Business statistics a first course 2nd edition sharpe test bank 1