Understandable Statistics Concepts and Methods 12th Edition by Charles Henry Brase – Test Bank

Understandable Statistics Concepts and Methods 12th Edition by Charles Henry Brase – Test Bank

Chapter 5 – The Binomial Probability Distribution and Related Topics

1. Give an example of a discrete random variable.

a.

The number of inches of rainfall in a county

b.

The number of beverages sold at a lemonade stand

c.

The number of gallons of concrete used at a construction site

d.

The time required for a runner to finish a marathon

e.

The temperature of a pot roast cooking in an oven

ANSWER:

b

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

False

LEARNING OBJECTIVES:

13.65 – Identify a discrete random variable

NOTES:

Concept

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/5/2013 3:46 AM

2. Give an example of a continuous random variable.

a.

The number of fish caught by a fishing boat

b.

The number of coins contained in a slot machine

c.

The number of traffic accidents in a city

d.

The number of gallons of water in a reservoir

e.

The number of tables sold at a furniture store

ANSWER:

d

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

False

LEARNING OBJECTIVES:

13.66 – Identify a continuous random variable

NOTES:

Concept

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/28/2014 3:09 AM

3. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Make a histogram for the probability distribution.

Age range (yr)

20–29

30–39

40–49

50–59

60–69

70–79

80+

Midpoint (x)

24.5

34.5

44.5

54.5

64.5

75.5

84.5

Percent of nurses

9.8%

5.6%

19.4%

24.9%

29.3%

9.3%

1.7%

a.

b.

c.

d.

e.

ANSWER:

c

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.67 – Identify the correct histogram given the data

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/28/2014 3:16 AM

4. What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Find the probability that a British nurse selected at random in 1851 would be 70 years of age or older. Round your answer to nearest thousandth.

Age range (yr)

20–29

30–39

40–49

50–59

60–69

70–79

80+

Midpoint (x)

24.5

34.5

44.5

54.5

64.5

75.5

84.5

Percent of nurses

5.7%

9.7%

19.5%

29.2%

25.0%

9.1%

1.8%

a.

0.091

b.

0

c.

0.109

d.

0.099

e.

0.105

ANSWER:

c

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.68 – Identify the probability for class boundary or higher

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/5/2013 3:50 AM

5. Compute the expected age μ of a British nurse in 1851. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Round your answer to nearest hundredth.

Age range (yr)

20–29

30–39

40–49

50–59

60–69

70–79

80+

Midpoint (x)

24.5

34.5

44.5

54.5

64.5

75.5

84.5

Percent of nurses

5.7%

9.6%

19.5%

29.1%

24.9%

9.0%

2.2%

a.

54.50

b.

59.50

c.

53.93

d.

53.96

e.

43.96

ANSWER:

d

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.69 – Compute the expected age m

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/13/2014 9:02 AM

6. Compute the standard deviation for ages of British nurses in 1851. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Round your answer to nearest hundredth.

Age range (yr)

20–29

30–39

40–49

50–59

60–69

70–79

80+

Midpoint (x)

24.5

34.5

44.5

54.5

64.5

75.5

84.5

Percent of nurses

5.8%

9.8%

19.6%

29.1%

24.9%

9.0%

1.8%

a.

13.69

b.

1.53

c.

3.27

d.

53.76

e.

17.25

ANSWER:

a

POINTS:

1

DIFFICULTY:

Difficult

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.70 – Identify the standard deviation

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/13/2014 9:12 AM

7. The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $3 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $35. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 717 cookies before the drawing. Lisa bought 31 cookies. What is the probability she will win the dinner for two? Write your answer as a fraction in simplest form, if one exists.

a.

b.

c.

d.

e.

none of these choices

ANSWER:

c

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.71 – Find the probability

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/28/2014 4:14 AM

8. The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $3 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $34. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 721 cookies before the drawing. Lisa bought 17 cookies. Lisa’s expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa’s expected earnings? Round your answer to the nearest cent.

a.

$0.82

b.

$2.00

c.

$33.20

d.

$0.80

e.

$34.00

ANSWER:

d

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.72 – Find expected values

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/5/2013 4:04 AM

9. The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $3 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $39. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 720 cookies before the drawing. Lisa bought 32 cookies. What is the probability she will not win the dinner for two? Write your answer as a fraction in simplest form, if one exists.

a.

b.

c.

d.

e.

none of these choices

ANSWER:

b

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.71 – Find the probability

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/28/2014 5:24 AM

10. The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $37. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 27 cookies. Lisa’s expected earnings can be found by multiplying the value of the dinner by the probability that she will win. How much did she effectively contribute to the hiking club?

a.

$23.55

b.

$49.41

c.

$52.61

d.

$25.63

e.

$25.61

ANSWER:

c

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.73 – Find out the effective contribution

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/5/2013 4:10 AM

11. Jim has a 5-year-old car in reasonably good condition. He wants to take out a $50,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:

x = age

5

6

7

8

9

P(accident)

0.01182

0.01282

0.01386

0.01513

0.01602

Jim is applying to a car insurance company for his car insurance policy. Using the probabilities that the car will have an accident in its 5th, 6th, 7th, 8th, or 9th year, and the $50,000 accident benefit, what is the expected loss to Car Insurance Company for the respective years? Round your answers to the nearest dollar.

a.

$591, $641, $693, $757, $801

b.

$581, $641, $693, $747, $801

c.

$591, $646, $693, $747, $801

d.

$581, $646, $693, $757, $801

e.

$591, $641, $693, $747, $801

ANSWER:

a

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.74 – Note the expected loss

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/5/2013 4:36 AM

12. Jim has a 5-year-old car in reasonably good condition. He wants to take out a $20,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:

x = age

5

6

7

8

9

P(accident)

0.01182

0.01282

0.01386

0.01602

0.01513

Jim is applying to a car insurance company for his term insurance policy. What would be the total expected loss to the insurance company over the years 5 through 9? Round your answer to the nearest dollar.

a.

$1390

b.

$1383

c.

$1388

d.

$1393

e.

$1386

ANSWER:

d

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.75 – What would be the total expected loss

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/5/2013 4:38 AM

13. Jim has a 5-year-old car in reasonably good condition. He wants to take out a $20,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:

x = age

5

6

7

8

9

P(accident)

0.01191

0.01292

0.01396

0.01503

0.01613

Jim is applying to a car insurance company for his car insurance policy. If the car insurance company wants to make a profit of $900 above the expected total losses, how much should it charge for the policy? Round your answer to the nearest dollar.

a.

$2297

b.

$2299

c.

$2301

d.

$2294

e.

$2292

ANSWER:

b

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.76 – What would be the charge

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/5/2013 4:41 AM

14. Jim has a 5-year-old car in reasonably good condition. He wants to take out a $20,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:

x = age

5

6

7

8

9

P(accident)

0.01182

0.01282

0.01386

0.01513

0.01602

Jim is applying to a car insurance company for his car insurance policy. If the car insurance company charges $7000 for the policy, how much profit does the company expect to make? Round your answer to the nearest dollar.

a.

$5604

b.

$5609

c.

$5602

d.

$5611

e.

$5607

ANSWER:

e

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.77 – Note the expected profit

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/5/2013 4:43 AM

15. Jim has a 5-year-old car in reasonably good condition. He wants to take out a $30,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:

x = age

5

6

7

8

9

P(accident)

0.01191

0.01292

0.01396

0.01503

0.01613

Jim is applying to a car insurance company for his car insurance policy. The expected loss to the car insurance company for the 5th, 6th, 7th, 8th, and 9th years would be $357.30, $387.60, $418.80, $450.90 or $483.90 respectively. What would be the total expected loss to the car insurance company over the years 5 through 9? Round your answer to the nearest dollar.

a.

$2097

b.

$2098

c.

$2099

d.

$2100

e.

$2096

ANSWER:

c

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.75 – What would be the total expected loss

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/5/2013 4:45 AM

16. Jim has a 5-year-old car in reasonably good condition. He wants to take out a $20,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:

x = age

5

6

7

8

9

P(accident)

0.01182

0.01282

0.01386

0.01513

0.01602

Jim is applying to a car insurance company for his car insurance policy. If the car insurance company wants to make a profit of $700 above the expected total losses of $1393, how much should it charge for the policy?

a.

$701

b.

$693

c.

$713

d.

$703

e.

$705

ANSWER:

d

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.76 – What would be the charge

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/13/2014 8:54 AM

17. Jim has a 5-year-old car in reasonably good condition. He wants to take out a $60,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:

x = age

5

6

7

8

9

P(accident)

0.01191

0.01292

0.01396

0.01503

0.01613

Jim is applying to a car insurance company for his car insurance policy. If the car insurance company charges $6000 for the policy and the expected total loss is $4197, how much profit does the company expect to make? Round your answer to the nearest dollar.

a.

$1803

b.

$1806

c.

$1801

d.

$1798

e.

$1804

ANSWER:

a

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.77 – Note the expected profit

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/13/2014 9:18 AM

18. A computer repair shop has two work centers. The first center examines the computer to see what is wrong and the second center repairs the computer. Let x₁ and x₂ be random variables representing the lengths of time in minutes to examine a computer (x₁) and to repair a computer (x₂). Assume x₁ and x₂ are independent random variables. Long-term history has shown the following mean and standard deviation for the two work centers:

Examine computer,

x₁

:

µ₁

=

28.1 minutes;

σ₁

=

7.5 minutes

Repair computer,

x₂

:

µ₂

=

90.7 minutes;

σ₂

=

15.3 minutes

Let W=x₁+x₂ be a random variable representing the total time to examine and repair the computer. Compute the mean and standard deviation of W. Round your answer to the nearest tenth.

a.

b.

c.

d.

e.

ANSWER:

b

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.78 – Compute mean and standard deviation

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/28/2014 6:26 AM

19. A computer repair shop has two work centers. The first center examines the computer to see what is wrong and the second center repairs the computer. Let and be random variables representing the lengths of time in minutes to examine a computer () and to repair a computer (). Assume and are independent random variables. Long-term history has shown the following mean and standard deviation for the two work centers:

Examine computer,

:

=

27.3 minutes;

=

7.5 minutes

Repair computer,

:

=

90.1 minutes;

=

15.3 minutes

Let be a random variable representing the total time to examine and repair the computer. Suppose it costs $1.80 per minute to examine the computer and $2.83 per minute to repair the computer. Then is a random variable representing the service charges (without parts). Compute the mean and standard deviation of V. Round your answer to the nearest tenth.

a.

b.

c.

d.

e.

ANSWER:

c

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.78 – Compute mean and standard deviation

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/6/2013 12:51 AM

20. A computer repair shop has two work centers. The first center examines the computer to see what is wrong and the second center repairs the computer. Let x₁ and x₂ be random variables representing the lengths of time in minutes to examine a computer (x₁) and to repair a computer (x₂). Assume x₁ and x₂ are independent random variables. Long-term history has shown the following mean and standard deviation for the two work centers:

Examine computer,

x₁

:

µ₁

=

27.2 minutes;

σ₁

=

7.6 minutes

Repair computer,

x₂

:

µ₂

=

90.6 minutes;

σ₂

=

15.5 minutes

Let W=x₁ +x₂ be a random variable representing the total time to examine and repair the computer. There is a flat rate of $1.80 per minute to examine the computer, and if no repairs are ordered, there is an additional $70 service charge. Let . Compute the mean and standard deviation of L.

a.

b.

c.

d.

e.

ANSWER:

b

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.78 – Compute mean and standard deviation

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/28/2014 6:35 AM

21. Richard has been given a 9-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. What is the value of p? (p is the value of success) Round your answer to the nearest tenth.

a.

9.0

b.

27.0

c.

3.0

d.

0.3

e.

2.7

ANSWER:

d

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.79 – Note the value of success

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/28/2014 6:59 AM

22. Richard has been given a 12-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. What is the value of n ?(n is the number of trials)

a.

0.4

b.

12.0

c.

4.8

d.

60.0

e.

2.4

ANSWER:

b

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.80 – Find the number of trials

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

3/28/2014 6:58 AM

23. Richard has been given a 10-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. What is considered the success?

a.

number of questions

b.

Richard answers a question correctly.

c.

number of questions answered

d.

Richard is unable to answer a question correctly.

e.

none of the choices

ANSWER:

b

POINTS:

1

DIFFICULTY:

Easy

QUESTION TYPE:

Multiple Choice

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.81 – Note the success

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/6/2013 2:22 AM

24. Richard has been given a 9-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. Assuming that Richard guesses on all 9 questions, find the probability that he will answer all questions correctly. Round your answer to the nearest thousandth.

a.

0.000

b.

0.250

c.

0.500

d.

0.028

e.

0.444

ANSWER:

a

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.71 – Find the probability

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/6/2013 2:24 AM

25. Richard has been given a 7-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. Assuming that Richard guesses on all 7 questions, find the probability that he will answer all questions incorrectly. Round your answer to the nearest thousandth.

a.

0.800

b.

0.500

c.

0.463

d.

0.210

e.

0.857

ANSWER:

d

POINTS:

1

DIFFICULTY:

Medium

QUESTION TYPE:

Multi-Mode (Multiple choice)

HAS VARIABLES:

True

LEARNING OBJECTIVES:

13.71 – Find the probability

NOTES:

Application

DATE CREATED:

11/4/2013 1:58 AM

DATE MODIFIED:

11/6/2013 2:25 AM