Exam 5: Randomness and Probability

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. A. Construct the contingency table. b. Are gender and participation in online auctions independent? Explain.

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Question 1

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a. Construct the contingency table.
\ $a. Construct the contingency table. \ b. Are gender and participation in online auctions independent? Explain. The conditional probability P(Yes Participated in Online Auction/Men) = 0.25 / 0.48 = 0.52 does not equals the marginal probability \mathrm { P } (Yes Participated in Online Auction) = 0.35 . No, participation in online auctions is not independent of gender.$

b. Are gender and participation in online auctions independent? Explain.
The conditional probability P(Yes Participated in Online Auction/Men) $= 0.25 / 0.48 =$ $0.52$ does not equals the marginal probability $\mathrm { P }$ (Yes Participated in Online Auction) $=$ $0.35$ . No, participation in online auctions is not independent of gender.

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?

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Question 2

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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?

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Question 3

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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 $\$ 50$ ?
$.01 ( 1 / 10 \times 1 / 10 )$ independence rule

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 gets $50? 10 30 10 30 10 20 10 50 10 20

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Question 4

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? Problem Resolved? HD cable TV Internet Phone Yes 123 350 77 No 115 122 63

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Question 5

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 big screen TVs and laptop computers from a leading electronics retailer are summarized in the table. A. What is the probability that a consumer purchases an extended warranty? b. What is the probability that a consumer purchases a big screen TV and an extended warranty? c. What is the probability that a consumer purchases an extended warranty given that he/she has purchased a big screen TV?

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Question 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. The probability That a cell phone sold last month did not have either a camera or a music player is

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Question 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?

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Question 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 big screen TVs and Laptop computers from a leading electronics retailer are summarized in the table. Which Of the following statement is true?

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Question 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 a digital camera and an extended warranty is

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Question 10

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

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Question 11

During a promotion, Christina's department store offers a mailing "scratch a winner - discount savings." After customers select the items they wish to purchase, they scratch Their discount sticker from the mailing to determine the discount they will receive. The Scratch 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 if the customer Scratches that slice! The probability that a customer gets a 10% or 20% discount is

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Question 12

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.

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Question 13

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

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Question 14

During a promotion, Christina's department store offers a mailing "scratch a winner - discount savings." After customers select the items they wish to purchase, they scratch their discount sticker from the mailing to determine the discount they will receive. The scratch 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 if the customer scratches that slice! 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?

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Question 15

Suppose you visit Christina's department store 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.

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Question 16

During a promotion, Christina's department store offers a mailing "scratch a winner - discount savings." After customers select the items they wish to purchase, they scratch Their discount sticker from the mailing to determine the discount they will receive. The Scratch 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 if the customer Scratches that slice! The probability that two customers in a row get a 20% discount is

(Multiple Choice)

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Question 17

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

(Multiple Choice)

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Question 18

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

(Multiple Choice)

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Question 19

A recent survey of local cell phone retailers showed that of all smart phones sold last month, 64% of buyers also owned a tablet of laptop, 28% also owned an iPod type music player and 22% owned both. A. What is the probability that a smart phone buyer also owned a tablet/ laptop or a music player? 5-1

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Question 20

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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

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

Data and Decisions

Displaying and Describing Categorical Data

Displaying and Describing Quantitative Data

Correlation and Linear Regression

Random Variables and Probability Models

The Normal and Other Continuous Distributions

Surveys and Sampling

Sampling Distributions and Confidence Intervals for Proportions

Testing Hypotheses About Proportions

Confidence Intervals and Hypothesis Tests for Means

Comparing Two Means

Inference for Counts: Chi-Square Tests

Inference for Regression

Multiple Regression

Introduction to Data Mining

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