Probability and Statistics for Business and Economics

0 / 2 pts

Q4.  A car wash is staffed with 10 attendants, with four attendants assigned to the first area and six attendants assigned to the second area.  After a customer exits the vehicle, the vehicle is rolled to the first area where two of the four attendants manually wash, rinse, and wax the vehicle.  The vehicle is then rolled to the second area where three of the six attendants perform detailing of the interior and exterior of the vehicle.  How many outcomes (combinations) with the attendants are possible as the vehicle completes the washing and detailing process? 

0 / 3 pts

Q5.  A coloring dye dispenser dispenses dye on pieces of fabric before the fabric is used to make clothing.  The dispenser has 8 different colors of dye and dispenses 5 different colors on each piece of fabric.  The order in which the dye is dispensed is important as each variation of the different dyes on the fabric is considered a different pattern.  For example, if the dye is dispensed in the pattern red, green, blue, orange, and yellow, this would be considered a different pattern from green, red, blue, orange, and yellow.  Given this information, how many different patterns are possible from a dye dispenser? 

0 / 2 pts

Q8.  To play Powerball in Virginia, a participant must purchase a $1 ticket, select six numbers from the digits 1 through 49, and then select a Powerball number from the digits 1 through 40. To determine the winning numbers for each game, lottery officials draw 6 white balls out a drum of 49 white balls numbered 1 through 49 and 1 red ball out of a drum of 40 red balls numbered 1 through 40.  To win the Powerball jackpot, a participant’s numbers must match the numbers on the 6 white balls in any order and must also match the number on the one (1) red Powerball.   If a very rich individual decided to spend $100 million purchasing unique tickets, what is the probability, to two decimal places, that the individual has the winning ticket?  (Note:  treat the selection of the six numbers and the Powerball as two separate steps)  

0 / 2 pts

Q9.  The head of a sales department with 90 sales associates, awards a sales bonus to sales associates who either complete more than $10,000 in sales in a week or is rated outstanding by 5 customers in one week.  During the past week, 18 associates completed more than $10,000 in sales and 12 associates were rated outstanding by at least 5 customers.  Four (4) of the 18 associates who completed more than $10,000 in sales were also rated as outstanding by at least 5 customers.   What is the probability, to two decimal places, that a randomly chosen associate will receive a bonus for the past week?  

0 / 2 pts

Q12.  The Chappel group owns and operates restaurants across the United States.  The group has seen that feedback from customers, which is posted online, affects the traffic of customers to the restaurants.  The group owns and operates restaurants in the South East, North East, and South West region.  Customers are given a coupon if the customers rate the restaurants on a scale of 1 - 5 stars, with a "1" star representing very dissatisfied and a "5" star rating representing very satisfied.  A manager at the group headquarters reviewed 60 ratings which were submitted by customers.   The review indicated that 20 of the customers  rated the restaurants from 1 to 3 stars.   There were 40 customers who provided a rating on the South East region.  There were 14 customers who rated the South East region from 1 to 3 stars.  There were 8 customers who rated the South East region as 5 stars.  If one of the 60 customer ratings is selected,  what is the probability, to two decimal places, of selecting a rating of  4 or 5 stars?   

0 / 2 pts

Q14.  The Chappel group owns and operates restaurants across the United States.  The group has seen that feedback from customers, which is posted online, affects the traffic of customers to the restaurants.  The group owns and operates restaurants in the South East, North East, and South West region.  Customers are given a coupon if the customers rate the restaurants on a scale of 1 - 5 stars, with a "1" star representing very dissatisfied and a "5" star rating representing very satisfied.  A manager at the group headquarters reviewed 60 ratings which were submitted by customers.   The review indicated that 20 of the customers  rated the restaurants from 1 to 3 stars.   There were 40 customers who provided a rating on the South East region.  There were 14 customers who rated the South East region from 1 to 3 stars.  There were 8 customers who rated the South East region as 5 stars.  If one of the 60 customer ratings is selected,  what is the probability, to two decimal places, of selecting a rating on the South East region or a rating of 4 or 5 stars?   

0 / 2 pts

Q15.  The Chappel group owns and operates restaurants across the United States.  The group has seen that feedback from customers, which is posted online, affects the traffic of customers to the restaurants.  The group owns and operates restaurants in the South East, North East, and South West region.  Customers are given a coupon if the customers rate the restaurants on a scale of 1 - 5 stars, with a "1" star representing very dissatisfied and a "5" star rating representing very satisfied.  A manager at the group headquarters reviewed 60 ratings which were submitted by customers.   The review indicated that 20 of the customers  rated the restaurants from 1 to 3 stars.   There were 40 customers who provided a rating on the South East region.  There were 14 customers who rated the South East region from 1 to 3 stars.  There were 8 customers who rated the South East region as 5 stars.  If one of the 60 customer ratings is selected,  what is the probability, to two decimal places of selecting a rating on the North East or South West region AND the rating is 4 or 5 stars?  

0 / 2 pts

Q18.  A well known athletic shoe brand would like to advertise a new line of shoes and matching apparel which targets 18- to 29-year-olds via social media. A 2018 study by the Pew Research Center found that 28% of U.S. adults (18 and older) do not use social media (Pew Research Center website).  Out of the total US adults (18 and older), the percentage of U.S. adults age 30 and older is 65%.  Assume that the percentage of the U.S. adult population that is either age 18–29 or uses social media is 75%.  What is the percentage of the US adult population age 30 and older that uses social media?  [NOTE: PLEASE DO NOT USE THE PERCENTAGE SIGN IN YOUR ANSWER.  IF YOUR ANSWER IS 25%, ENTER THE VALUE 25 AS YOUR ANSWER.]

0 / 2 pts

Q19.  A well known athletic shoe brand would like to advertise a new line of shoes and matching apparel which targets 18- to 29-year-olds via social media. A 2018 study by the Pew Research Center found that 28% of U.S. adults (18 and older) do not use social media (Pew Research Center website).  Out of the total US adults (18 and older), the percentage of U.S. adults age 30 and older is 65%.  Assume that the percentage of the U.S. adult population that is either age 18–29 or uses social media is 75%.  What is the percentage of the US adult population age 18 to 29  that uses social media? [NOTE: PLEASE DO NOT USE THE PERCENTAGE SIGN IN YOUR ANSWER.  IF YOUR ANSWER IS 25%, ENTER THE VALUE 25 AS YOUR ANSWER.]

0 / 2 pts

Q20.  A well known athletic shoe brand would like to advertise a new line of shoes and matching apparel which targets 18- to 29-year-olds via social media. A 2018 study by the Pew Research Center found that 28% of U.S. adults (18 and older) do not use social media (Pew Research Center website).  Out of the total US adults (18 and older), the percentage of U.S. adults age 30 and older is 65%.  Assume that the percentage of the U.S. adult population that is either age 18–29 or uses social media is 75%.  What is the percentage of the US adult population age 18 to 29 that does not use social media? [NOTE: PLEASE DO NOT USE THE PERCENTAGE SIGN IN YOUR ANSWER.  IF YOUR ANSWER IS 25%, ENTER THE VALUE 25 AS YOUR ANSWER.]

0 / 2 pts

Q21.  A well known athletic shoe brand would like to advertise a new line of shoes and matching apparel which targets 18- to 29-year-olds via social media. A 2018 study by the Pew Research Center found that 28% of U.S. adults (18 and older) do not use social media (Pew Research Center website).  Out of the total US adults (18 and older), the percentage of U.S. adults age 30 and older is 65%.  Assume that the percentage of the U.S. adult population that is either age 18–29 or uses social media is 75%.  What is the percentage of the US adult population age 30 and older that does not use social media? [NOTE: PLEASE DO NOT USE THE PERCENTAGE SIGN IN YOUR ANSWER.  IF YOUR ANSWER IS 25%, ENTER THE VALUE 25 AS YOUR ANSWER.]

2 / 2 pts

Q22.  A local city recreational center offers swimming lessons to children from age 6 to 10 years old.  At the end of the lessons, the children are tested on a number of swimming tasks such as flotation, strokes, breathing etc.  At the end of the test, the children are classified as either being able to swim or not being able to swim.  Some parents have voiced concerns that their daughters are being unfairly classified as not being able to swim.  The recreational center disputes this and believes there's no connection between the ability to swim and the gender of the child.  The center has offered the following information for the boys and girls who have completed the lessons and were tested over the past three years:  So far, 900 children have completed the lessons, of which 630 have been girls.  The records indicate that 189 girls have been classified as unable to swim whereas only 81 boys have been classified as unable to swim.  This would very much seem to support the parents' contention.  If a child is randomly selected from the total number of children who have completed the training, what is the probability, to two decimal places, that the child is unable to swim? 

0 / 2 pts

Q25.  A local city recreational center offers swimming lessons to children from age 6 to 10 years old.  At the end of the lessons, the children are tested on a number of swimming tasks such as flotation, strokes, breathing etc.  At the end of the test, the children are classified as either being able to swim or not being able to swim.  Some parents have voiced concerns that their daughters are being unfairly classified as not being able to swim.  The recreational center disputes this and believes there's no connection between the ability to swim and the gender of the child.  The center has offered the following information for the boys and girls who have completed the lessons and were tested over the past three years:  So far, 900 children have completed the lessons, of which 630 have been girls.  The records indicate that 189 girls have been classified as unable to swim whereas only 81 boys have been classified as unable to swim.  This would very much seem to support the parents' contention.  If a child is randomly selected from the total number of children who have completed the training, and child selected is unable to swim, what is the probability, to two decimal places, that the child selected is a girl?  

2 / 2 pts

Q26.  A local city recreational center offers swimming lessons to children from age 6 to 10 years old.  At the end of the lessons, the children are tested on a number of swimming tasks such as flotation, strokes, breathing etc.  At the end of the test, the children are classified as either being able to swim or not being able to swim.  Some parents have voiced concerns that their daughters are being unfairly classified as not being able to swim.  The recreational center disputes this and believes there's no connection between the ability to swim and the gender of the child.  The center has offered the following information for the boys and girls who have completed the lessons and were tested over the past three years:  So far, 900 children have completed the lessons, of which 630 have been girls.  The records indicate that 189 girls have been classified as unable to swim whereas only 81 boys have been classified as unable to swim.  This would very much seem to support the parents' contention.  Which of the following is most accurate about the results of the lessons?

The concerns of the parents are accurate because the probability of a child randomly selected as a girl who is unable to swim is much higher than the probability of a child randomly selected as a boy who is unable to swim

The recreation center's beliefs are accurate as independence has been established through the probability calculations

The recreation center's beliefs are accurate as many more girls are able to swim than boys

The concerns of the parents are accurate as the number of girls who are unable to swim is more than twice as many as the number of boys who are unable to swim

0 / 2 pts

Q27.   A local city recreational center offers swimming lessons to children from age 6 to 10 years old.  At the end of the lessons, the children are tested on a number of swimming tasks such as flotation, strokes, breathing etc.  At the end of the test, the children are classified as either being able to swim or not being able to swim.  Some parents have voiced concerns that their daughters are being unfairly classified as not being able to swim.  The recreational center disputes this and believes there's no connection between the ability to swim and the gender of the child.  The center has offered the following information for the boys and girls who have completed the lessons and were tested over the past three years:  So far, 900 children have completed the lessons, of which 630 have been girls.  The records indicate that 189 girls have been classified as unable to swim whereas only 81 boys have been classified as unable to swim.  This would very much seem to support the parents' contention.  Which of the following statements would support independence?

The probability of randomly choosing a boy who can swim is equal to the probability of randomly choosing a girl who can't swim

The probability of randomly choosing a boy who can swim is the same as the probability of randomly choosing a girl who can swim

The probability of randomly choosing a child who can swim is the same as randomly choosing a child, and the child is a girl, and the probability of the girl being able to swim

The probability of randomly choosing a boy is the same as the probability of randomly choosing a girl

0 / 2 pts

Q28.  Two events, F and G, are  mutually exclusive .  If the probability of F occurring,  P(F) is 0.25, and the probability of G occurring, P(G) is 0.30, what is the numerical value, to two decimal places, of P(F | G)?  Think about what mutually exclusive means, and think about the probability function that you are trying to calculate.

2 / 2 pts

Q29.  During her 30 minute lunch break, Janet can go to a nearby restaurant and dine in and return to her office, which takes about 30 minutes.  Janet can also decide to go to a nearby park and eat her lunch which she prepared at home.  This also takes about 30 minutes.  Which of the following statements would be true for Janet on any given day, if dining in at the restaurant and eating at the park are considered as two events?

Dining in and eating at the park are mutually exclusive and dependent events

Dining in and eating at the park are non-mutually exclusive events only

Dining in and eating at the park are independent events only

Dining in and eating at the park are mutually exclusive events only

Dining in and eating at the park are dependent events only

Dining in and eating at the park are mutually exclusive and independent events

0 / 3 pts

Q31.  Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States. One of the most common tests for the potential detection of prostate cancer is the prostate-specific antigen (PSA) test.  The test is known to have a high false-positive rate for cancer because the presence of PSA is not necessarily an indicator of cancer.  [However,  the presence of PSA is considered a warning sign and might lead a doctor to request a biopsy to confirm the presence of cancer.  My personal correction to this quote since I have had prostate cancer.]   Suppose there is a .05 probability that a male patient has prostate cancer before testing. The probability of a false-positive test is .85, and the probability of a false-negative (no indication of cancer when cancer is actually present) is .35.  What is the probability, to two decimal places, that the male patient has prostate cancer if the PSA test comes back positive?

0 / 3 pts

Q34.  Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States. One of the most common tests for the potential detection of prostate cancer is the prostate-specific antigen (PSA) test.  The test is known to have a high false-positive rate for cancer because the presence of PSA is not necessarily an indicator of cancer.  [However,  the presence of PSA is considered a warning sign and might lead a doctor to request a biopsy to confirm the presence of cancer.  My personal correction to this quote since I have had prostate cancer.]   Suppose there is a .05 probability that a male patient has prostate cancer before testing. The probability of a false-positive test is .85, and the probability of a false-negative (no indication of cancer when cancer is actually present) is .35.  What is the probability, to two decimal places, that the male patient does not have prostate cancer if the PSA test comes back negative?

0 / 2 pts

Q35.  The National Center for Health Statistics, housed within the U.S. Centers for Disease Control and Prevention (CDC), tracks the number of adults in the United States who have health insurance. According to this agency, the uninsured rates for Americans in 2018 are as follows: 5.1% of those under the age of 18, 12.4% of those ages 18–64, and 1.1% of those 65 and older do not have health insurance (CDC website). Approximately 22.8% of Americans are under age 18, and 61.4% of Americans are ages 18–64.  Given that a person is an uninsured American, what is the probability, to two decimal places, that the person is age 18 - 64?

0 / 2 pts

Q38.   An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities of finding oil: 

P (high-quality oil)  = 0.60

P (medium-quality oil) = 0.30

P (No oil) =0.10

After drilling 200 feet into the first well, the company performed a soil test.  The soil test indicated the probabilities of finding the particular type of soil identified by the test below.  

P(soil | high-quality oil) = 0.30

P(soil | medium-quality oil) = 0.70

P (soil | no oil) = 0.30

After the soil test is completed, what is the revised probability of finding oil, to two decimal places?

0 / 2 pts

Q40.  An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities of finding oil: 

P (high-quality oil)  = 0.60

P (medium-quality oil) = 0.30

P (No oil) =0.10

After drilling 200 feet into the first well, the company performed a soil test.  The soil test indicated the probabilities of finding the particular type of soil identified by the test below.  

P(soil | high-quality oil) = 0.30

P(soil | medium-quality oil) = 0.70

P (soil | no oil) = 0.30

After the soil test is completed, what is the revised (posterior) probability of finding medium-quality oil, to two decimal places?

Quiz Score: 9 out of 50

0.99

0.03

0.47

0.47

0

46.8

26.25

8.75

18.2

0.3

0.21

36

0.3

252

0.3

0.05

0.08

0.39

0.57

56