CHAPTER 6 RESERVE PROBLEMS

The following problems have been reserved for your use in assignments and testing and do not

appear in student versions of the text.

Reserve Problems Chapter 6 Section 1 Problem 1

An independent research was made asking 500 people about their bank deposits. Using the data

in the table, calculate the deposit sample mean and deposit sample standard deviation.

SOLUTION

First of all, we need to multiple each deposit amount by the number of depositors:

Now calculate the deposit mean:

Amount of deposit, $

( )

i

x

1000

3000

3500

7000

15000

Number of depositors

( )

i

n

96

107

130

89

78

Reserve Problems Chapter 6 Section 1 Problem 2

A consignment of 100 half-inch nuts was released from the factory. The diameters of 10

randomly taken nuts were measured. Calculate the sample mean and sample standard deviation

using the data in the table.

Number

of nut

1

2

3

4

5

6

7

8

9

10

Diameter,

inch

0.4983

0.5030

0.4982

0.4986

0.5010

0.5009

0.4984

0.4993

0.5014

0.5010

SOLUTION

Sample average:

Sample variance:

122.5001

j

j

n

x

=

=

Reserve Problems Chapter 6 Section 1 Problem 3

During the second part of April Chicago Bulls had 6 games with Boston Celtics. The number of

points, scored in each game is in the table. Calculate the sample mean and sample standard

deviation using the data in the table.

No

1

2

3

4

5

6

Number of

points

90

95

87

95

97

83

SOLUTION

Sample average:

Sample variance:

Reserve Problems Chapter 6 Section 1 Problem 4

An independent research was made in a dog shelter to measure the heights of dogs of different

breeds. Eight dogs were evaluated for this experiment. The results are shown in the table below.

Calculate the sample mean and sample standard deviation using the data in the table.

Number

of dog

1

2

3

4

5

6

7

8

Dog’s

height,

m

0.75

0.15

0.35

0.60

0.62

0.58

0.75

0.76

SOLUTION

Sample average:

Sample variance:

Reserve Problems Chapter 6 Section 1 Problem 5

Suppose that you add 2 to all observations in a sample. How does this change the sample mean?

How does it change the sample standard deviation?

SOLUTION

Let

x

be the original observations, and

10

xx

=+

be the shifted ones, then

Reserve Problems Chapter 6 Section 1 Problem 6

The United States has an aging infrastructure as witnessed by several recent disasters, including

the I-35 bridge failure in Minnesota. Most states inspect their bridges regularly and report their

condition (on a scale from 1–7) to the public.

Here are the condition numbers from a sample of 30 bridges

5.08

5.44

6.66

5.07

6.04

5.43

4.83

4.00

4.41

3.61

7.00

5.72

3.48

6.43

3.97

4.19

6.26

5.27

5.26

5.48

4.95

5.76

4.93

5.61

4.66

7.00

5.57

3.42

5.91

4.54

Find the sample mean and the sample standard deviation of these condition numbers.

SOLUTION

Sample mean:

Sample variance:

Reserve Problems Chapter 6 Section 1 Problem 7

In an attempt to measure the effects of acid rain, researchers measured the pH (7 is neutral and

values below 7 are acidic) of water collected from rain in Ingham County, Michigan.

5.47

5.37

5.38

4.63

4.34

5.02

3.71

4.96

4.64

5.94

5.54

5.39

4.16

5.62

4.57

5.90

5.48

4.57

4.57

4.51

4.62

4.56

4.61

4.32

3.98

5.56

4.15

3.98

5.65

3.10

5.04

4.62

4.88

4.34

4.16

4.64

5.12

3.71

4.80

5.59

Find the sample mean and sample standard deviation of these measurements.

SOLUTION

Sample mean:

Reserve Problems Chapter 6 Section 2 Problem 1

An independent research was made to calculate the mean weight of elder people in Russia. 50

men and women were interviewed for this research. Construct a stem-and-leaf diagram for the

data. Calculate the median and quartiles of these data. All values are in kg.

74

89

84

85

57

81

78

79

77

83

94

82

57

75

82

77

60

79

76

97

99

70

97

57

69

84

92

82

91

85

76

92

76

63

69

58

64

59

89

91

96

85

80

59

58

94

57

79

89

87

SOLUTION

(a) Construct a stem-and-leaf diagram.

Stem

Leaf

5

7 7 7 7 8 8 9 9

Reserve Problems Chapter 6 Section 2 Problem 2

An independent research was made to calculate the mean weight of elder people in Russia. 50

men and women were interviewed for this research. Calculate the sample median, mode, and

mean of the data. Explain how these three measures of location describe different features of the

data. All values are in kg.

74

89

84

85

57

81

78

79

77

83

94

82

57

75

82

77

60

79

76

97

99

70

97

57

69

84

92

82

91

85

76

92

76

63

69

58

64

59

89

91

94

85

80

59

58

94

57

79

89

87

SOLUTION

The median is halfway between 25th and 26th, so it is the average of the 25th and 26th values and

it equals 79.5.

Reserve Problems Chapter 6 Section 2 Problem 3

The table represents the answers of 80 respondents to the survey “How much sports trainings do

you have every year?” carried out among college students. Construct a stem-and-leaf diagram for

the data. Calculate the median and quartiles of these data.

129

157

154

191

192

142

188

126

128

180

190

166

157

147

155

154

200

128

167

143

131

156

153

168

149

144

155

188

149

142

160

149

184

187

169

161

157

134

122

173

188

183

178

148

135

188

187

166

121

177

169

182

158

169

146

173

133

189

183

143

148

121

181

145

189

120

122

189

146

190

128

142

189

131

199

182

197

148

157

140

SOLUTION

(a) Construct a stem-and-leaf diagram.

12

0 1 1 2 2 6 8 8 8 9

13

1 1 3 4 5

Reserve Problems Chapter 6 Section 2 Problem 4

The table represents the answers of 80 respondents to the survey “How much sports trainings do

you have every year?” carried out among college students. Calculate the sample median, mode,

and mean of the data. Explain how these three measures of location describe different features of

the data.

129

157

154

191

192

142

188

126

128

180

190

166

157

147

155

154

200

128

167

143

131

156

153

168

149

144

155

188

149

142

160

149

184

187

169

161

157

134

122

173

188

183

178

148

135

188

187

166

121

177

169

182

158

169

146

173

138

189

183

143

148

121

181

145

189

120

122

189

146

190

128

142

189

131

199

182

197

148

157

140

SOLUTION

The median is halfway between 40th and 41th, so it is the average of the 40th and 41th values and

it equals 157.

Reserve Problems Chapter 6 Section 2 Problem 5

The United States has an aging infrastructure as witnessed by several recent disasters, including

the I-35 bridge failure in Minnesota. Most states inspect their bridges regularly and report their

condition (on a scale from 1–7) to the public.

Here are the condition numbers from a sample of 30 bridges in New York State:

5.08

5.44

6.66

5.07

6.80

5.43

4.83

4.00

4.41

4.38

7.00

5.72

4.53

6.43

3.97

4.19

6.26

6.72

5.26

5.48

4.95

6.33

4.93

5.61

4.66

7.00

5.57

3.42

5.18

4.54

Choose the correct steam-and-leaf diagram.

A

N = 30

Leaf Unit = 0.10

1

3

4

2

3

9

6

4

0134

12

4

556899

(7)

5

0012444

11

5

567

8

6

234

5

6

678

2

7

00

B

N = 30

Leaf Unit = 0.010

1

3

4

2

3

9

6

4

0134

12

4

556899

(7)

5

0012444

11

5

567

8

6

234

5

6

678

2

7

00

C

N = 30

Leaf Unit = 0.10

1

3

4

2

3

9

6

4

0134

13

4

556899

(5)

5

0012444

11

5

567

8

6

234

5

6

678

2

7

00

D

N = 30

Leaf Unit = 0.010

1

3

4

2

3

9

6

4

0134

12

4

556899

(5)

5

0012444

11

5

567

8

6

234

5

6

678

1

7

00

Do any of the bridges appear to have unusually good or poor ratings? If so, compute the mean

with and without these bridges and comment.

SOLUTION

(a) N = 30

(b) One particular bridge has poor rating of 3.4.

Reserve Problems Chapter 6 Section 2 Problem 6

In an attempt to measure the effects of acid rain, researchers measured the pH (7 is neutral and

values below 7 are acidic) of water collected from rain in Ingham County, Michigan.

5.47

5.37

5.38

4.63

5.37

3.74

3.71

4.96

4.64

5.11

5.65

5.39

4.16

5.62

4.57

4.64

5.48

4.57

4.57

4.51

4.86

4.56

4.61

4.32

3.98

5.70

4.15

3.98

5.65

3.10

5.04

4.62

4.51

4.34

4.16

4.64

5.12

3.71

4.64

5.59

Select the correct stem-and-leaf diagram.

A

N=40. Leaf Unit = 0.10

1

3

1

4

3

777

6

3

99

9

4

111

11

4

33

17

4

555555

(7)

4

6666666

16

4

89

14

5

011

11

5

3333

7

5

445

4

5

6667

B

N=40. Leaf Unit = 0.010

1

3

1

4

3

777

6

3

99

9

4

111

11

4

33

17

4

555555

(7)

4

6666666

16

4

89

14

5

011

11

5

3333

7

5

445

4

5

6667

C

N=40. Leaf Unit = 0.10

1

3

1

4

3

777

6

3

99

9

4

111

11

4

33

17

4

555555

(6)

4

666666

16

4

89

14

5

011

11

5

3333

7

5

445

4

5

6667

D

N=40. Leaf Unit = 0.10

1

3

1

3

3

77

6

3

999

9

4

111

11

4

33

17

4

555555

(6)

4

666666

16

4

89

14

5

0111

10

5

333

7

5

445

4

5

6667

Many scientists consider rain with pH below 5.3 to be acid rain. What percentage of these

samples could be consider as acid rain?

SOLUTION

Reserve Problems Chapter 6 Section 2 Problem 7

The following data represent the yield on 90 consecutive batches of ceramic substrate to which a

metal coating has been applied by a vapor-deposition process.

94.1

86.1

95.3

84.9

88.8

84.6

94.4

84.1

93.2

90.4

94.1

78.3

86.4

83.6

96.1

83.7

90.6

89.1

97.8

89.6

85.1

85.4

98.0

82.9

91.4

87.3

93.1

90.3

84.0

89.7

85.4

87.3

88.2

84.1

86.4

93.1

93.7

87.6

86.6

86.4

86.1

90.1

87.6

94.6

87.7

85.1

91.7

84.5

95.1

95.2

94.1

96.3

90.6

89.6

87.5

90.0

86.1

92.1

94.7

89.4

90.0

84.2

92.4

94.3

96.4

91.1

88.6

90.1

85.1

87.3

93.2

88.2

92.4

84.1

94.3

90.5

86.6

86.7

86.4

90.6

82.6

97.3

95.6

91.2

83.0

85.0

89.1

83.1

96.8

88.3

Select the correct stem-and-leaf display for these data.

A

N=90. Leaf Unit = 1

1

7e|8

7

8t|223333

21

8f|44444444555555

38

8s|66666666667777777

(11)

8e|88888999999

41

9z|00000000001111

27

9t|22223333

19

9f|444444445555

7

9s|666677

1

9e|8

B

N=90. Leaf Unit = 10

1

7e|8

7

8t|223333

21

8f|44444444555555

38

8s|66666666667777777

(13)

8e|88888999999

41

9z|00000000001111

27

9t|22223333

19

9f|444444445555

7

9s|666677

1

9e|8

C

N=90. Leaf Unit = 1

1

7e|8

6

8t|223333

14

8f|44444444555555

17

8s|66666666667777777

(11)

8e|88888999999

14

9z|00000000001111

8

9t|22223333

12

9f|444444445555

6

9s|666677

1

9e|8

D

N=90. Leaf Unit = 10

1

7e|8

7

8t|223333

20

8f|4444444555555

37

8s|6666666667777777

(11)

8e|88888999999

39

9z|000000000111

27

9t|22223333

18

9f|44444445555

7

9s|666677

1

9e|8

Calculate the median of these data. Calculate the quartiles of these data.

Reserve Problems Chapter 6 Section 2 Problem 8

The net energy consumption (in billions of kilowatt-hours) for countries in Asia in 2003 was as

follows

Billions of Kilowatt-Hours

Afghanistan

1.04

Australia

200.66

Bangladesh

16.20

Burma

6.88

China

1671.23

Hong Kong

38.43

India

519.04

Indonesia

101.80

Japan

946.27

Korea, North

17.43

Korea, South

303.33

Laos

3.30

Malaysia

73.63

Mongolia

2.91

Nepal

2.30

New Zealand

37.03

Pakistan

71.54

Philippines

44.48

Singapore

30.89

Sri Lanka

6.80

Taiwan

154.34

Thailand

107.34

Vietnam

36.92

Total

4393.8

Select the correct stem-and-leaf display of these data.

A

N=23, Leaf Unit = 100

(18)

0|000000000000000111

5

0|23

3

0|5

2

0|9

1

1|6

B

N=24, Leaf Unit = 100

(18)

0|000000000000000111

6

0|23

4

0|5

3

0|9

2

1|6

1

4|3

C

N=23, Leaf Unit = 100

(17)

0|00000000000000111

5

0|23

3

0|5

2

0|9

1

1|6

D

N=24, Leaf Unit = 100

(19)

0|0000000000000000111

5

0|23

3

0|5

2

0|9

1

1|6

Compute the sample mean, sample standard deviation, and sample median:

SOLUTION

Do not use the total as an observation. There are 23 observations. (N=23, Leaf Unit = 100)

Sample mean:

Reserve Problems Chapter 6 Section 2 Problem 9

The United States Golf Association tests golf balls to ensure that they conform to the rules of

golf. Balls are tested for weight, diameter, roundness, and overall distance. The overall distance

test is conducted by hitting balls with a driver swung by a mechanical device nicknamed “Iron

Byron” after the legendary great Byron Nelson, whose swing the machine is said to emulate.

Following are 100 distances (in yards) achieved by a particular brand of golf ball in the overall

distance test.

261.3

259.4

265.7

270.6

274.2

261.4

254.5

283.7

258.1

270.5

255.1

268.9

267.4

253.6

234.3

263.2

254.2

270.7

233.7

263.5

244.5

251.8

259.5

257.5

257.7

272.6

253.7

262.2

252.0

280.3

274.9

233.7

237.9

274.0

264.5

244.8

264.0

268.3

272.1

260.2

255.8

260.7

245.5

279.6

237.8

278.5

273.3

263.7

241.4

260.6

230.3

272.7

261.0

260.0

279.3

252.1

244.3

272.2

248.3

278.7

236.0

271.2

279.8

245.6

241.2

251.1

267.0

273.4

247.7

254.8

272.8

270.5

254.4

232.1

271.5

242.9

273.6

256.1

251.6

256.8

273.0

240.8

276.6

264.5

264.5

226.8

255.3

266.6

250.2

255.8

285.3

255.4

240.5

255.0

273.2

251.4

276.1

277.8

266.8

268.5

Select the correct stem-and-leaf diagram for these data.

A

N=100, Leaf Unit = 1

1

22|6

5

23|2334

8

23|677

16

24|00112444

20

24|5578

33

25|0111122334444

46

25|5555556677899

(15)

26|000011123334444

39

26|56677888

31

27|0000112222233333444

12

27|66788999

4

28|003

1

28|5

B

N=100, Leaf Unit = 1

1

22|6

5

23|2334

8

23|677

16

24|00112444

20

24|5578

33

25|0111122334444

46

25|5555556677899

(14)

26|00011123334444

39

26|56677888

31

27|0000112222233333444

12

27|66788999

4

28|003

1

28|5

C

N=100, Leaf Unit = 1

1

22|6

5

23|2334

8

23|677

16

24|00112444

20

24|5578

33

25|0111122334444

46

25|5555556677899

(16)

26|0000111123334444

39

26|56677888

31

27|0000112222233333444

12

27|66788999

4

28|003

1

28|5

D

N=100, Leaf Unit = 1

1

22|6

5

23|2334

8

23|677

16

24|00112444

20

24|5578

34

25|01111122334444

45

25|555556677899

(15)

26|000011123334444

40

26|566778888

30

27|000011222233333444

12

27|66788999

4

28|003

1

28|5

Compute the sample mean, sample standard deviation, and the sample median.

What is the 90th percentile of distances?

SOLUTION

Sample mean:

Reserve Problems Chapter 6 Section 2 Problem 10

A semiconductor manufacturer produces devices used as central processing units in personal

computers. The speed of the devices (in megahertz) is important because it determines the price

that the manufacturer can charge for the devices. The following table contains measurements on

120 devices.

680

669

719

699

670

710

722

663

658

634

720

690

677

669

700

718

690

681

702

696

692

690

694

660

649

675

701

721

683

735

688

763

672

698

659

704

681

679

691

683

705

746

706

649

668

672

690

724

652

720

660

695

701

724

668

698

668

660

680

739

717

727

653

637

660

693

679

682

724

642

704

695

704

652

664

702

661

720

695

670

656

718

660

648

683

723

710

680

684

705

681

748

697

703

660

722

662

644

683

695

678

674

656

667

683

691

680

685

681

715

665

676

665

675

655

659

720

675

697

663

Select the correct stem-and-leaf diagram for these data

A

N=120, Leaf Unit = 1.0

2

63|47

7

64|24899

16

65|223566899

35

66|0000001233455788899

48

67|002245567899

(17)

68|00001111233333458

55

69|0000112345555677889

36

70|011223444556

24

71|0057889

17

72|000012234447

5

73|59

3

74|68

1

76|3

B

N=120, Leaf Unit = 1.0

2

63|47

7

64|24899

16

65|223566899

35

66|0000001233455788899

48

67|002245567899

(19)

68|0000111112333333458

55

69|0000112345555677889

36

70|011223444556

24

71|0057889

17

72|000012234447

5

73|59

3

74|68

1

76|3

C

N=120, Leaf Unit = 1.0

2

63|47

7

64|24899

16

65|223566899

34

66|000001233455788899

48

67|002245567899

(17)

68|00001111233333458

55

69|0000112345555677889

36

70|011223444556

24

71|0057889

16

72|00012234447

5

73|59

3

74|68

1

76|3

D

N=120, Leaf Unit = 10

2

63|47

7

64|24899

16

65|223566899

35

66|0000001233455788899

48

67|002245567899

(17)

68|00001111233333458

55

69|0000112345555677889

36

70|011223444556

24

71|0057889

17

72|000012234447

5

73|59

3

74|68

1

76|3

Compute the sample mean, the sample standard deviation, and the sample median.

What percentage of the devices has a speed exceeding 700 MHz?

SOLUTION

Sample mean:

Reserve Problems Chapter 6 Section 3 Problem 1

The following times (in seconds) were captured for athletes running the 100 meter race.

12.1

13.2

11.8

14.7

15.2

16.4

14.9

14.8

14.8

14.7

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