Practice Exam 1

MATH 103/GRACEY Name___________________________________

PRACTICE EXAM/CHAPTERS 1-3

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and

likely.

1) Andrew rolled a die five times and got a six every time.

A) Possible and likely

B) Possible, but very unlikely

C) Impossible

1)

2) Lori rolled three dice and got a total of 2.

A) Possible, but very unlikely

B) Possible and likely

C) Impossible

2)

3) When Amina took a four-day Thanksgiving vacation in Seattle, it rained every day.

A) Possible, but very unlikely

B) Impossible

C) Possible and likely

3)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

4) Use the data in the table to answer the question. The x-values are amounts of saturated fat

(in grams) in various regular two-ounce muffins. The y-values are amounts of saturated

fat (in grams) in various "low fat" two-ounce muffins.

Amounts of Saturated Fat in Regular and Low-Fat Muffins

x 5.8 6.5 4.2 5.7 5.2 3.8

y 1.2 2.1 2.1 0.7 2.2 0.9

Is each x-value matched with a corresponding y-value? That is, is each x-value associated

with the corresponding y-value in some meaningful way? If the x- and y-values are not

matched, does it make sense to use the difference between each x-value and the y-value

that is in the same column?

4)

5) The table shows the weights, in pounds, of seven subjects before and after following a

particular diet for two months. Assume that the x-values are the weights before the diet

and the y-values are the weights after the diet.

Subject A B C D E F G

Before 195 159 167 169 162 166 174

After 188 150 165 174 148 168 162

Are the x-values matched with the corresponding y-values? That is, is each x-value

associated with the corresponding y-value in some meaningful way? If the x- and

y-values are matched, does it make sense to use the difference between each x-value and

the y-value that is in the same column? Why or why not?

5)

1

Form a conclusion about statistical significance. Do not make any formal calculations. Either use the results provided or

make subjective judgments about the results.

6) Charlie's teacher claims that he does not study and just guesses on exams. On an exam

with 201 true-false questions, Charlie answered 53.7% of the questions correctly.

Calculations using these results show that if he were really just guessing, there would be

roughly 1 chance in 7 that he would do this well. Is there statistically significant evidence

against the teacher's claim that Charlie is just guessing? Why or why not?

6)


7) An article stated that last year 807 people taking a certain medication suffered from serious

side effects while this year, after the medication had been modified, only 391 suffered

serious side effects. What information is missing? Why would it be important to include

this information?

7)


Determine whether the given value is a statistic or a parameter.

8) A sample of 120 employees of a company is selected, and the average age is found to be 37 years.

A) Statistic B) Parameter

8)

9) After taking the first exam, 15 of the students dropped the class.

A) Parameter B) Statistic

9)

10) A health and fitness club surveys 40 randomly selected members and found that the average

weight of those questioned is 157 lb.

A) Statistic B) Parameter

10)

Determine whether the given value is from a discrete or continuous data set.

11) The number of freshmen entering college in a certain year is 621.

A) Discrete B) Continuous

11)

12) The temperature of a cup of coffee is 67.3°F.


12)

13) The number of limbs on a 2-year-old oak tree is 21.

A) Continuous B) Discrete

13)

14) The weight of Bill's pack as he sets off on a backpacking trip is 48.3 lb.


14)

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.

15) The temperatures of eight different plastic spheres.

A) Ordinal B) Ratio C) Nominal D) Interval

15)

16) The sample of spheres categorized from softest to hardest.

A) Ratio B) Nominal C) Interval D) Ordinal

16)

17) Salaries of college professors.

A) Ordinal B) Nominal C) Ratio D) Interval

17)

2

18) Temperatures of the ocean at various depths.

A) Nominal B) Ratio C) Interval D) Ordinal

18)


Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.

19) An employee at the local ice cream parlor asks three customers if they like chocolate ice

cream.

19)

Use critical thinking to develop an alternative conclusion.

20) A study shows that adults who work at their desk all day weigh more than those who do

not. Conclusion: Desk jobs cause people to gain weight.

20)

Use critical thinking to address the key issue.

21) An airline company advertises that 100% of their flights are on time after checking 5

randomly selected flights and finding that these 5 were on time.

21)

22) You plan to make a survey of 200 people. The plan is to talk to every 10th person coming

out of the school library. Is there a problem with your plan?

22)

23) A researcher published this survey result: "74% of people would be willing to spend 10

percent more for energy from a non-polluting source". The survey question was

announced on a national radio show and 1,200 listeners responded by calling in. What is

wrong with this survey?

23)

24) A company accused of downsizing workers defended itself with the following statement:

"Yes, we were forced to lay off 20% of our workforce last year, but this year we increased

our workforce by 20%, and we therefore now have the same number of employees as

before the layoff." What is the flaw in this argument?

24)


Perform the requested conversions. Round decimals to the nearest thousandth and percents to the nearest tenth of a

percent, if necessary.

25) Convert the fraction 4

9 to an equivalent decimal and percentage.

A) 0.444, 44.4% B) 0.564, 56.4% C) 0.444, 4.44% D) 0.564, 564%

25)

26) Convert 0.6 to an equivalent fraction and percentage.

A)2

5, 6% B)

3

5, 60% C)

2

5, 60% D)

3

5, 6%

26)

27) Convert 0.296 to an equivalent fraction and percent.

A)36

125, 29.6% B)

37

125, 29.6% C)

36

125, 2.96% D)

37

125, 2.96%

27)

28) Convert 2.5 to an equivalent fraction and percent.

A) 21

2, 25% B) 2, 25% C) 2, 250% D) 2

1

2, 250%

28)

3

Solve the problem.

29) A gardener has 78 clients, 10% of whom are businesses. Find the number of business clients.

A) 8 clients B) 10 clients C) 76 clients D) 70 clients

29)

30) Alex and Juana went on a 116-mile canoe trip with their class. On the first day they traveled 29

miles. What percent of the total distance did they canoe?

A) 0.25% B) 400% C) 25% D) 4%

30)

31) On a test, 86% of the questions are answered correctly. If 215 questions are correct, how many

questions are on the test?

A) 250 B) 86 C) 43 D) 40

31)



32) A bus company claims that in the past year it has reduced the number of late departures of

buses by 100%. What is wrong with this statement?

32)


Determine whether the given description corresponds to an observational study or an experiment.

33) A marketing firm does a survey to find out how many people use a product. Of the one hundred

people contacted, fifteen said they use the product.

A) Observational study B) Experiment

33)

34) A clinic gives a drug to a group of ten patients and a placebo to another group of ten patients to

find out if the drug has an effect on the patients' illness.


34)

35) A political pollster reports that his candidate has a 10% lead in the polls with 10% undecided.


35)

36) A doctor performs several diagnostic tests to determine the reason for a patient's illness.


36)

Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience.

37) 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348,

and 481 students respectively.

A) Cluster

B) Random

C) Systematic

D) Stratified

E) Convenience

37)

38) A sample consists of every 49th student from a group of 496 students.

A) Convenience

B) Random

C) Stratified

D) Cluster

E) Systematic

38)

4

39) A pollster uses a computer to generate 500 random numbers, then interviews the voters

corresponding to those numbers.

A) Random

B) Cluster

C) Convenience

D) Stratified

E) Systematic

39)

40) An education researcher randomly selects 48 middle schools and interviews all the teachers at each

school.

A) Systematic

B) Random

C) Convenience

D) Stratified

E) Cluster

40)

41) A researcher interviews 19 work colleagues who work in his building.

A) Stratified

B) Convenience

C) Systematic

D) Cluster

E) Random

41)


42) An education expert is researching teaching methods and wishes to interview teachers from a

particular school district. She randomly selects ten schools from the district and interviews all of the

teachers at the selected schools. Does this sampling plan result in a random sample? Simple

random sample? Explain.

A) No; no. The sample is not random because teachers in small schools are more likely to be

selected than teachers in larger schools. It is not a simple random sample because some

samples are not possible, such as a sample that includes teachers from schools that were not

selected.

B) Yes; yes. The sample is random because all teachers have the same chance of being selected. It

is a simple random sample because all samples have the same chance of being selected.

C) Yes; no. The sample is random because all teachers have the same chance of being selected. It

is not a simple random sample because some samples are not possible, such as a sample that

includes teachers from schools that were not selected.

D) No; yes. The sample is not random because teachers in small schools are more likely to be

selected than teachers in larger schools. It is a simple random sample because all samples

have the same chance of being selected.

42)

5

43) A researcher obtains an alphabetical list of the 2560 students at a college. She uses a random

number generator to obtain 50 numbers between 1 and 2560. She chooses the 50 students

corresponding to those numbers. Does this sampling plan result in a random sample? Simple

random sample? Explain.

A) No; yes. The sample is not random because not all students have the same chance of being

selected. It is a simple random sample because all samples of 50 students have the same

chance of being selected.

B) Yes; yes. The sample is random because all students have the same chance of being selected. It

is a simple random sample because all samples of 50 students have the same chance of being

selected.

C) No; no. The sample is not random because not all students have the same chance of being

selected. It is not a simple random sample because some samples are not possible, such as a

sample containing the the first 50 students on the list.

D) Yes; no. The sample is random because all students have the same chance of being selected. It

is not a simple random sample because some samples are not possible, such as a sample

containing the first 50 students on the list.

43)

Identify the type of observational study (cross-sectional, retrospective, prospective).

44) A statistical analyst obtains data about ankle injuries by examining a hospital's records from the

past 3 years.

A) Cross-sectional B) Prospective C) Retrospective D) None of these

44)

45) A researcher plans to obtain data by following those in cancer remission since January of 2005.

A) Prospective B) Cross-sectional C) Retrospective D) None of these

45)

46) A town obtains current employment data by polling 10,000 of its citizens this month.

A) Prospective B) Cross-sectional C) Retrospective D) None of these

46)



47) In a clinical trial for a new headache medication, participants are randomly assigned to a

treatment group or a placebo group. They do not know whether they are receiving the

medication or a placebo. However the doctors administering the medication and

evaluating the results do know which participants are receiving the medication. This

experiment is blind but not double blind. Explain what this means and why the absence of

double blinding could cause a problem.

47)


48) The frequency distribution below summarizes employee years of service for Alpha Corporation.

Determine the width of each class.

Years of service Frequency

1-5 5

6-10 20

11-15 25

16-20 10

21-25 5

26-30 3

A) 10 B) 6 C) 5 D) 4

48)

6


Solve the problem.

49) Using a strict interpretation of the relevant criteria characterizing a normal

distribution,does the frequency distribution below appear to have a normal distribution?

Does the distribution appear to be normal if the criteria are interpreted very loosely?

Closing Share

Price Frequency

0-5 2

6-10 5

11-15 16

16-20 28

49)


Construct the cumulative frequency distribution that corresponds to the given frequency distribution.

50)

Speed

Number

of cars

0-29 4

30-59 16

60-89 60

90-119 20

A)

Speed

Cumulative

Frequency

Less than 30 4

Less than 60 20

Less than 90 80

Less than120 100

B)

Speed

Cumulative

Frequency

Less than 30 0.04

Less than 60 0.20

Less than 90 0.80

Less than120 1.00

C)

Speed

Cumulative

Frequency

0-29 4

30-59 20

60-89 80

90-119 100

D)

Speed

Cumulative

Frequency

Less than 30 100

Less than 60 80

Less than 90 82

Less than120 4

50)

7


51) The frequency distribution for the weekly incomes of students with part-time jobs is given below.

Construct the corresponding relative frequency distribution. Round relative frequencies to the

nearest hundredth of a percent if necessary.

Income ($) Frequency

200-300 68

301-400 69

401-500 79

501-600 87

More than 600 11

A)

Income ($)

Relative

Frequency

201-300 15.5%

301-400 22.1%

401-500 31.3%

501-600 16.2%

More than600 14.9%

B)

Income ($)

Relative

Frequency

200-300 24.76%

301-400 27.97%

401-500 3.53%

501-600 21.38%

More than 600 24.84%

C)

Income ($)

Relative

Frequency

200-300 12.5%

301-400 20.1%

401-500 37.3%

501-600 15.2%

More than 600 14.9%

D)

Income ($)

Relative

Frequency

200-300 21.66%

301-400 21.97%

401-500 25.16%

501-600 27.71%

More than 600 3.50%

51)


Use the given data to construct a frequency distribution.

52) A medical research team studied the ages of patients who had strokes caused by stress. The

ages of 34 patients who suffered stress strokes were as follows.

29 30 36 41 45 50 57 61 28 50 36 58

60 38 36 47 40 32 58 46 61 40 55 32

61 56 45 46 62 36 38 40 50 27

Construct a frequency distribution for these ages. Use 8 classes beginning with a lower class

limit of 25.

Age Frequency

52)

8



53) A nurse measured the blood pressure of each person who visited her clinic. Following is a

relative-frequency histogram for the systolic blood pressure readings for those people aged

between 25 and 40. The blood pressure readings were given to the nearest whole number.

Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading

between 110 and 139 inclusive?

A) 59% B) 39% C) 75% D) 89%

53)

54) The histogram below represents the number of television sets per household for a sample of U.S.

households. How many households are included in the histogram?

1 2 3 4 5

50

40

30

20

10

Number of TV Sets

Fre

qu

ency

1 2 3 4 5

50

40

30

20

10

Number of TV Sets

Fre

qu

ency

A) 110 B) 95 C) 90 D) 100

54)

9


55) In a survey, 26 voters were asked their ages. The results are shown below. Construct a

histogram to represent the data (with 5 classes beginning with a lower class limit of 19.5

and a class width of 10). What is the approximate age at the center?

43 56 28 63 67 66 52 48 37 51 40 60 62

66 45 21 35 49 32 53 61 53 69 31 48 59

55)

56) Suppose that you construct a histogram and a relative frequency histogram corresponding

to a particular frequency table. In what ways will the two histograms be similar? In what

ways will they differ?

56)

Solve the problem.

57) The frequency table below shows the amount of weight loss during the first month of a diet

program for both males and females. Compare the results by constructing two frequency

polygons on the same axes, and determine whether there appears to be a significant

difference between the two genders.

Weight (lb) Frequency (males)

5-7

8-10

11-13

14-16

17-19

20-22

2

9

18

13

4

1

Weight (lb) Frequency (females)

5-7

8-10

11-13

14-16

17-19

20-22

4

3

19

5

15

1

5 10 15 20 25

20

18

16

14

12

10

8

6

4

2

5 10 15 20 25

20

18

16

14

12

10

8

6

4

2

57)

10


Construct the dotplot for the given data.

58) Attendance records at a school show the number of days each student was absent during the year.

The days absent for each student were as follows.

0 2 3 4 2 3 4 6 7 2 3 4 6 9 8

A) B)

C) D)

58)

Use the data to create a stemplot.

59) The attendance counts for this season's basketball games are listed below.

227 239 215 219

221 233 229 233

235 228 245 231

A)

21

22

23

24

5 9

1 7 8 9

1 3 3 5 9

5

B)

21

22

23

24

5 7 9

1 8 9

1 3 3 5 9

5

59)

11

60) The following data consists of the weights (in pounds) of 15 randomly selected women and the

weights of 15 randomly selected men. Construct a back-to-back stemplot for the data.

Women:

128 150 118 166 142

122 137 110 175 152

145 126 139 111 170

Men:

140 153 199 186 169

136 176 162 196 155

173 190 141 166 153

A)

Men Women

11 0 1

12 2 6 8

6 13 7 9

1 0 14 2 5

5 3 3 15 0 2 4

9 6 2 16 6

6 3 17 0 5

9 6 18

9 6 19

B)

Men Women

11 0 1 8

12 2 6 8

6 13 7 9

1 0 14 2 5

5 3 3 15 0 2

9 6 2 16 6

6 3 17 0 5

6 18

9 6 0 19

60)

Find the original data from the stemplot.

61)

Stem Leaves

6 5 8

7 1 8

8 5 5

A) 61, 65, 61, 78, 88, 85 B) 65, 61, 68, 71, 81, 85

C) 65, 68, 71, 71, 85, 85 D) 65, 68, 71, 78, 85, 85

61)


62) The table contains data from a study of daily study time for 40 students from Statistics 101.

Construct an ogive from the data.

Minutes on

homework

Number of

students

Relative

frequency

Cumulative

frequency

0-15 2 0.05 2

16-30 4 0.10 6

31-45 8 0.20 14

46-60 18 0.45 32

61-75 4 0.10 36

76-90 4 0.10 40

Cu

mu

lati

ve

Fre

qu

ency

Cu

mu

lati

ve

Fre

qu

ency

50

45

40

35

30

25

20

15

10

5

0

15.5 30.5 45.5 60.5 75.5 90.5

Homework Time (minutes)

62)

12

A)

Rel

ativ

e F

req

uen

cyR

elat

ive

Fre

qu

ency

100

90

80

70

60

50

40

30

20

10

0

15.5 30.5 45.5 60.5 75.5 90.5


B)

Rel

ativ

e F

req

uen

cyR

elat

ive

Fre

qu

ency

100

90

80

70

60

50

40

30

20

10

0

15.5 30.5 45.5 60.5 75.5 90.5


C) D)

Fre

qu

ency

Fre

qu

ency

100

90

80

70

60

50

40

30

20

10

0

15.5 30.5 45.5 60.5 75.5 90.5


Solve the problem.

63) 240 casino patrons, were interviewed as they left the casino. 72 of them said they spent most of the

time playing the slots. 72 of them said they played blackjack. 36 said they played craps. 12 said

roulette. 12 said poker. The rest were not sure what they played the most. Construct a Pareto chart

to depict the gaming practices of the group of casino goers. Choose the vertical scale so that the

relative frequencies are represented.

63)

13

A) B)

C) D)

64) A car dealer is deciding what kinds of vehicles he should order from the factory. He looks at his

sales report for the preceding period. Choose the vertical scale so that the relative frequencies are

represented.

Vehicle Sales

Economy 34

Sports 8.5

Family 59.5

Luxury 17

Truck 51

Construct a Pareto chart to help him decide.

64)

14

A) B)

C) D)

Construct a pie chart representing the given data set.

65) The following figures give the distribution of land (in acres) for a county containing 66,000 acres.

Forest Farm Urban

9900 6600 49,500

A) B)

65)

15

Use the pie chart to solve the problem.

66) A survey of the 4571 vehicles on the campus of State University yielded the following pie chart.

9%

16% 35%

8%

4%

28%

What percent of the vehicles are hatchbacks?

A) 35% B) 28% C) 160% D) 8%

66)

Use the given paired data to construct a scatterplot.

67) x -2 -8 -5 -1 -8 2 -6 6 -4 -2

y -6 -1 -8 2 4 3 -10 4 -2 -6

x-10 10

y

10

-10

x-10 10

y

10

-10

A)

x-10 10

y

10

-10

x-10 10

y

10

-10

B)

x-10 10

y

10

-10

x-10 10

y

10

-10

67)

16

C)

x-10 10

y

10

-10

x-10 10

y

10

-10

D)

x-10 10

y

10

-10

x-10 10

y

10

-10



68) Use the high closing values of Naristar Inc. stock from the years 1990 - 2001 to construct a

time-series graph. (Let x = 0 represent 1990 and so on.) Identify a trend.

Year High Year High

1990 42 1996 47

1991 40 1997 60

1992 31 1998 61

1993 42 1999 57

1994 44 2000 54

1995 47 2001 30

x

y

x

y

68)

17

69) An annual survey sent to retail store managers contained the question "Did your store

suffer any losses due to employee theft?" The responses are summarized in the table for

two years, 2000 and 2005. Construct a multiple bar graph of the data, then describe any

trends.

Employee

Theft

Percentage

in 2000

Percentage

in 2005

Yes 49 32

No 51 68

Totals 100 100

69)

70) A television manufacturer sold three times as many televisions in 2005 as it did in 1995. To

illustrate this fact, the manufacturer draws a graph as shown below. The television on the

right is three times as tall and three times as wide as the television on the left. Why is this

graph misleading? What visual impression is created by the graph?

70)

18


Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than

is present in the original data values.

71) The weights (in pounds) of six dogs are listed below. Find the mean weight.

13 21 75 21 134 60

A) 54 lb B) 53.5 lb C) 64.8 lb D) 54.5 lb

71)

Find the median for the given sample data.

72) The ages (in years) of the eight passengers on a bus are listed below.

6 4 25 19 26 49 36 33

Find the median age.

A) 25 yr B) 25.5 yr C) 26 yr D) 24.5 yr

72)

Find the mode(s) for the given sample data.

73) 77 52 32 52 29 77

A) 77 B) 53.2 C) 52 D) 77, 52

73)

Find the midrange for the given sample data.

74) A meteorologist records the number of clear days in a given year in each of 21 different U.S. cities.

The results are shown below. Find the midrange.

72 143 52 84 100 98 101

120 99 121 86 60 59 71

125 130 104 74 83 55 169

A) 112 days B) 110.5 days C) 98 days D) 117 days

74)


Find the mean and median for each of the two samples, then compare the two sets of results.

75) A comparison is made between summer electric bills of those who have central air and

those who have window units.

May June July Aug Sept

Central $32 $64 $80 $90 $65

Window $15 $84 $99 $120 $40

75)


Find the mean of the data summarized in the given frequency distribution.

76) A company had 80 employees whose salaries are summarized in the frequency distribution below.

Find the mean salary.

Salary ($) Employees

5,001-10,000 16

10,001-15,000 14

15,001-20,000 15

20,001-25,000 17

25,001-30,000 18

A) $16,143.75 B) $17,500 C) $17,937.50 D) $19,731.25

76)

19

Solve the problem.

77) A student earned grades of 91, 76, 92, and 79 on her four regular tests. She earned a grade of 79 on

the final exam and 85 on her class projects. Her combined homework grade was 87. The four

regular tests count for 40% of the final grade, the final exam counts for 30%, the project counts for

10%, and homework counts for 20%. What is her weighted mean grade? Round to one decimal

place.

A) 84.2 B) 84.1 C) 82.4 D) 83.4

77)

Find the range for the given sample data.

78) Rich Borne teaches Chemistry 101. Last week he gave his students a quiz. Their scores are listed

below.

22 31 47 29 31 12 48 41 50 56 37 22

A) 44 B) 9 C) 12 D) 56

78)

Find the variance for the given data. Round your answer to one more decimal place than the original data.

79) 19 11 12 7 11

A) 19.0 B) 15.2 C) 49.0 D) 18.9

79)

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in

the original data.

80) The top nine scores on the organic chemistry midterm are as follows.

37, 24, 53, 49, 44, 63, 28, 49, 30

A) 13.9 B) 13.0 C) 5.2 D) 12.3

80)

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal

place.

81) Compare the variation in heights to the variation in weights of thirteen-year old girls. The heights

(in inches) and weights (in pounds) of nine randomly selected thirteen-year old girls are listed

below.

Heights (inches): 59.2 61.4 62.4 64.7 60.1 58.3 64.6 63.7 66.1

Weights (pounds): 86 94 92 119 96 90 123 98 139

A) Heights: 4.4%

Weights: 17.6%

There is substantially more variation in the weights than in the heights of the girls.

B) Heights: 4.1%

Weights: 16.7%


C) Heights: 11.5%

Weights: 6.6%

There is substantially more variation in the heights than in the weights of the girls.

D) Heights: 4.6%

Weights: 18.4%


81)

20

Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.

82) When investigating times required for drive-through service, the following results (in seconds)

were obtained.

Restaurant A 120 67 89 97 124 68 72 96

Restaurant B 115 126 49 56 98 76 78 95

A) Restaurant A: 57 sec; 493.98 sec2; 22.23 sec

Restaurant B: 56 sec; 727.98 sec2; 32.89 sec

There is more variation in the times for restaurant B.

B) Restaurant A: 57 sec; 493.98 sec2; 22.23 sec



C) Restaurant A: 75 sec; 493.98 sec2; 22.23 sec



D) Restaurant A: 57 sec; 793.98 sec2; 28.18 sec


There is more variation in the times for restaurant A.

82)

Find the standard deviation of the data summarized in the given frequency distribution.

83) A company had 80 employees whose salaries are summarized in the frequency distribution below.

Find the standard deviation.

Salary (dollars) Employees

5,001-10,000 14

10,001-15,000 13

15,001-20,000 18

20,001-25,000 18

25,001-30,000 17

A) $6969.4 B) $7526.9 C) $7317.8 D) $7736.0

83)

Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth.

84) The heights in feet of people who work in an office are as follows.

6.0 5.5 5.9 5.4 5.8 5.6 5.7 6.2 5.6 5.6

A) 1.2 B) 0.2 C) 0.1 D) 0.5

84)

Use the empirical rule to solve the problem.

85) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120

mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a

systolic blood pressure between 96 mmHg and 144 mmHg?

A) 68% B) 99.99% C) 95% D) 99.7%

85)

Solve the problem.

86) The ages of the members of a gym have a mean of 47 years and a standard deviation of 10 years.

What can you conclude from Chebyshev's theorem about the percentage of gym members aged

between 32 and 62?

A) The percentage is at most 55.6% B) The percentage is approximately 33.3%

C) The percentage is at least 33.3% D) The percentage is at least 55.6%

86)

21

Solve the problem. Round results to the nearest hundredth.

87) Scores on a test have a mean of 75 and a standard deviation of 9. Michelle has a score of 84.

Convert Michelle's score to a z-score.

A) -9 B) -1 C) 9 D) 1

87)

88) A department store, on average, has daily sales of $28,993.06. The standard deviation of sales is $

1000. On Tuesday, the store sold $34,199.86 worth of goods. Find Tuesday's z score. Was Tuesday

an unusually good day?

A) 5.52, yes B) 5.21, yes C) 5.47, no D) 4.17, no

88)

Find the number of standard deviations from the mean. Round your answer to two decimal places.

89) The test scores on the Chapter 7 mathematics test have a mean of 66 and a standard deviation of 13.

Andrea scored 89 on the test. How many standard deviations from the mean is that?

A) 1.77 standard deviations above the mean B) 1.77 standard deviations below the mean

C) 0.60 standard deviations below the mean D) 0.60 standard deviations above the mean

89)

Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual.

Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth

if necessary.

90) A body temperature of 96.5° F given that human body temperatures have a mean of 98.20° F and a

standard deviation of 0.62°.

A) -2.8; unusual B) -1.7; not usual

C) -2.8; not unusual D) 2.8; unusual

90)

Determine which score corresponds to the higher relative position.

91) Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score

of 688 on a test with a mean of 493 and a standard deviation of 150?

A) Both scores have the same relative position.

B) A score of 688

C) A score of 92

91)

Find the percentile for the data value.

92) Data set: 53 45 39 69 66 72 44;

data value: 53

A) 20 B) 50 C) 43 D) 57

92)

Find the indicated measure.

93) Use the given sample data to find Q3.

49 52 52 52 74 67 55 55

A) 6.0 B) 67.0 C) 61.0 D) 55.0

93)

22

Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.

94) The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below.

Construct a boxplot for the data set.

310 320 450 460 470 500 520 540

580 600 650 700 710 840 870 900

1000 1200 1250 1300 1400 1720 2500 3700

A) B)

C) D)

94)

Construct a modified boxplot for the data. Identify any outliers.

95) The weights (in ounces) of 27 tomatoes are listed below.

1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6

2.6 2.6 2.7 2.7 2.7 2.8 2.8 2.8 2.9

2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2

A) Outliers: 1.7 oz, 3.6 oz, 4.2 oz

B) Outlier: 4.2 oz

C) No outliers

D) Outliers: 1.7 oz, 4.2 oz

95)

23


96) For data which are heavily skewed to the right, P10 is likely to be closer to the median than P90.

True or false?

A) True B) False

96)

97) If all the values in a data set are converted to z-scores, the shape of the distribution of the z-scores

will be bell-shaped regardless of the distribution of the original data. True or false?

A) True B) False

97)

98) In a data set containing n values, the 67th percentile can be found as follows:

P67 = 67

100 · n.

True or false?

A) False B) True

98)

99) Which of the following statements regarding percentiles is true? (More than one statement may be

true).

A : In any data set, P90 is greater than P80

B: In any data set, P10 + P90

2 is equal to Q2

C: In a set of 20 test scores, the percentile of the second highest score is 95

A) B B) A C) C D) All of the above

99)

24

Answer KeyTestname: PRACTICE EXAM 1

1) B

2) C

3) C

4) The x-values are not matched with the y-values, so it does not make sense to use the differences between each x-value

and the y-value that is in the same column.

5) The x-values are matched with the corresponding y-values. It makes sense to use the difference between each x-value

and the y-value that is in the same column. Both represent weights measured in pounds and both are associated with

the same person. The x-value is the weight of a person before the diet and the y-value in the same column is the

weight of the same person after the diet. The difference represents the amount of weight lost (or gained) by that

person.

6) No; The exam result of 53.7% is not substantially greater than 50%. Even if Charlie were just guessing, he could easily

do this well just by chance.

7) There is no context to the data. The article should include the number of people taking the medication last year and

this. More important than the number suffering serious side effects is the percentage of those taking the medication

that suffer side effects. Although fewer people suffered side effects this year, it is possible (if fewer people are taking

the medication this year) that the percentage suffering side effects has actually increased.

8) A

9) A

10) A

11) A

12) B

13) B

14) B

15) D

16) D

17) C

18) C

19) Sample: the 3 selected customers; population: all customers; not representative

20) Desk job workers are confined to their chairs for most of their work day. Other jobs require standing or walking

around which burns calories. It is probably the lack of exercise that causes higher weights, not the desk job itself. Avoid

causality altogether by saying lack of walking and exercise is associated with higher weights.

21) The sample was too small.

22) People who don't go to the library are excluded.

23) This is a voluntary response sample. The survey is based on voluntary, self-selected responses and therefore has

serious potential for bias.

24) Answers will vary. Possible answer: This is a misleading use of percentages, as 20% of the reduced workforce is

smaller than 20% of the original workforce. The company therefore did not hire as many new workers as it originally

laid off. The size of the current workforce is therefore smaller than the size of the workforce before the layoffs.

25) A

26) B

27) B

28) D

29) A

30) C

31) A

32) A reduction of 100% would mean that the company had reduced the number of late departures to zero which is not

plausible.

33) A

34) B

35) A

25


36) B

37) D

38) E

39) A

40) E

41) B

42) C

43) B

44) C

45) A

46) B

47) This experiment is blind because participants do not know whether they are receiving the treatment or a placebo. This

will allows investigators to determine whether the treatment effect is significantly different from the placebo effect.

However, the experiment is not double blind because the doctors administering the medication and evaluating the

results know which participants are receiving the medication. The doctors may not be impartial and their evaluation

and analysis of results could be influenced by their knowledge of which participants are receiving the treatment.

48) C

49) No; no; The frequencies do not increase, reach a maximum, and then decrease.

50) A

51) D

52)

Age Frequency

25-29 3

30-34 3

35-39 6

40-44 4

45-49 5

50-54 3

55-59 5

60-64 5

53) C

54) D

55) The approximate age at the center is 50.

56) The two histograms will have the same shape. They will also have the same scale on the horizontal axis. They will

differ only in the scales on the vertical axis: the histogram will show frequencies on the vertical axis while the relative

frequency histogram will show relative frequencies.

26


57) There does not appear to be a significant difference.

weight5 10 15 20 25

freq20

18

16

14

12

10

8

6

4

2

weight5 10 15 20 25

freq20

18

16

14

12

10

8

6

4

2

58) B

59) A

60) B

61) D

62) C

63) C

64) A

65) B

66) A

67) D

68) Trend: Answers will vary. Possible answer: High closing stock values show a decrease from 1990 through 1992, after

which the value of the stock rose through 1998. Another decrease occurred in 1999 and continued through 2001.

x1 2 3 4 5 6 7 8 9 10 11

y

80

70

60

50

40

30

20

10

x1 2 3 4 5 6 7 8 9 10 11

y

80

70

60

50

40

30

20

10

27


69) Losses due to employee theft have decreased from 2000 to 2005.

70) The area of the television on the right is nine times (not three times) the area of the television on the left. The graph

gives the visual impression that sales in 2005 were nine times the sales in 1995.

71) A

72) B

73) D

74) B

75) Central air: mean = $66.20; median = $65

Window unit: mean = $71.60; median = $84

Window units appear to be significantly more expensive.

76) C

77) D

78) A

79) A

80) B

81) A

82) B

83) A

84) B

85) C

86) D

87) D

88) B

89) A

90) A

91) C

92) C

93) C

94) D

95) D

96) A

97) B

98) A

99) B

28

Practice Exam 1

Documents

systolic blood

lower class

answer key

simple random

sampling plan

relative frequency

pie chart

relative frequencies