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Study Island
Copyright © 2013 Study Island - All rights reserved.
Generation Date: 01/18/2013
Generated By: Erica Ginnetti
Cumulative Frequency Plots
1. A contractor designed and built a subdivision. It took 6 months for the new subdivision to
reach 100 percent occupancy. The following cumulative percentage plot shows the percentage of
homes in the subdivision sold over the 6 month period.
What percentage of the homes were sold in the 4th month?
A. 50% of homes
B. 30% of homes
C. 75% of homes
D. 20% of homes
E. 80% of homes
Stemplots
2. The stemplot below shows the number of points scored in each game by the Tigers and the
Bears in one football season.
Points Scored
Tigers
Bears
7730
77440
7310
0
1
2
00337
0047
011448
221
3
5
Which of the following is true regarding the data sets above?
I.
The mean of the Tigers' scores is greater than the mean of the Bears' scores.
II.
The median of the Tigers' scores is less than the median of the Bears' scores.
III.
The range of the Tigers' scores is less than the range of the Bears' scores.
A. I and III
B. I and II
C. II and III
D. I only
E. All statements are true.
Histograms
3. The histograms below show the finishing times for a swim team's first competition and last
competition of a season.
Which of the following are true regarding the data sets above?
I.
The first competition's distribution is skewed left, and the last competition's distribution
is skewed left.
II.
The first competition's distribution is skewed right, and the last competition's distribution
is skewed right.
III.
The first competition's distribution is skewed left, and the last competition's distribution
is skewed right.
IV.
The first competition's distribution is skewed right, and the last competition's distribution
is skewed left.
V.
The data set for first competition contains an outlier.
A. I and V
B. V only
C. II only
D. I only
E. II and V
Data Collection
4. Tom is planting a garden. He plants three identical tomato plants in the same soil. Each plant
receives the same amount of sunlight and water. The first tomato plant receives store-bought
fertilizer. The second tomato plant receives homemade fertilizer. The third tomato plant does not
receive any fertilizer.
Which of the following methods is being used to investigate the effect of different fertilizers on
the rate of growth of the tomato plants?
A. observational study
B. separation study
C. survey
D. controlled experiment
Categorical Data
5. Sam opens a new sandwich shop. The shop has two speciality sandwiches: Sam's Turkey and
Sam's Ham. The monthly sales over a four month period are shown in the bar charts below.
What can be concluded about the popularity of each sandwich from the information above?
Sam's Turkey sandwich grew in popularity, and Sam's Ham sandwich declined in
A. popularity.
The number of Sam's Ham sandwiches sold exceeds the number of Sam's Turkey
B. sandwiches sold over the four month period.
Sam's Ham sandwich and Sam's Turkey sandwich maintained their popularity over the four
C. month period.
There is not enough information to make conclusions regarding the popularity of the
D. sandwiches.
Sam's Ham sandwich grew in popularity, and Sam's Turkey sandwich declined in
E. popularity.
Probability
6. Mark has 13 shirts in his closet. He has 6 long-sleeve shirts that are solid, and he has 10 shirts
that are solid. What is the probability that a shirt has long sleeves given that it is solid?
A.
B.
C.
D.
E.
Central Tendency and Spread
7. What is the mean of the number set below?
39.6 , 55.9 , 63.5 , 35.1 , 49.2 , 30.4 , 61 , 58.7
A. 39.34
B. 49.175
C. 52.55
D. 56.2
Stemplots
8. The stemplot below shows the ages of the employees at Jan's Restaurant.
Employee Age
1
2
3
4
5
6
66789
0001239
578
5
Which of the following is true regarding the data set above?
I.
II.
III.
IV.
The data is skewed left.
The data is skewed right.
The data is symmetric.
The data possesses a gap.
A. I and IV
B. II and IV
C. III only
D. II only
E. I only
Independent and Dependent Variables
9. A contractor currently has 11 construction workers working on a building. When the building
is finished, it will have 20 stories. If he increases the number of workers to 44, the building will
be done four times as quickly. Which statement best describes the time it takes to complete the
building?
A.
The time it takes to complete the building is both an independent and a dependent variable.
B.
C.
D.
E.
The time it takes to complete the building is both a dependent and a constant variable.
The time it takes to complete the building is the constant variable.
The time it takes to complete the building is the dependent variable.
The time it takes to complete the building is the independent variable.
Dotplots
10. The dotplot below shows the number of scholarship applications submitted by a group of
seniors.
Scholarship Applications
0
1
2
3
4
5
6
7
*
* * * * * *
* * * * * * *
* * * *
* * * * *
* * *
Which of the following is true regarding the data set above?
I.
II.
III.
IV.
The mean of the data is 3.5.
The range of the data is 6.
The data is symmetric.
The data possesses a gap.
A. II and IV
B. I only
C. III only
D. IV only
E. I and IV
Dotplots
11. The dotplot below shows the number of goals scored per game by the Raiders in a single
season.
Number of Goals Scored Per Game
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
0
1
2
3
4
*
5
6
7
8
9
10
Find the mean of the data above.
A. 4
B. 2.6
C. 2.8
D. 1.8
E. 2
The Normal Distribution
12. The sitting height (from the bottom of the seat to the top of the person's head) of male drivers
is normally distributed with a mean of 36 inches and a standard deviation of 1.4 inches as shown
below.
If a car company wants to design a vehicle so that 99.9% of men fit in the driver's seat, how high
from the bottom of the seat must they make the roof?
A. 31.8 in.
B. 40.2 in.
C. 37.4 in.
D. 38.8 in.
Independent and Dependent Variables
13. On average, the more years of education a person has, the higher the salary he or she will
have. What is the dependent variable in this statement?
A. salary
B. number of years of education
C. number of years spent working at the same company
D. position in a company
E.
The patient's fever is the independent variable.
Scatterplots
14. An ice cream company has discovered that the number of ice cream cones sold in one hour is
related to the temperature outside. A collection of data from two different stores on the outside
temperature and number of cones sold produced the dotplot below.
Without finding the equations, compare the regression models for Store A's data and Store B's
data.
The models will have the same slope but different intercepts because of an influential
A.
point.
B.
The models will have a different slopes and different intercepts because of an influential
point. Store A's slope will be greater than Store B's slope.
C. The models will be the same because the data points are the same.
The models will have a different slopes and different intercepts because of an influential
D.
point. Store A's slope will be less than Store B's slope.
E.
The models will have the same intercepts but different slopes because of an influential
point. Store A's slope will be less than Store B's slope.
Central Tendency and Spread
15. Ron is a waiter at a restaurant. He worked five shifts this week and made $69, $77, $71, $90,
and $73 in tips during each shift respectively. What is the mean for his tips during a shift?
A. $76
B. $71
C. $90
D. $77
Box Plots
16. Which of the following box plots is skewed left?
W.
X.
Y.
Z.
A. W
B. There are no box plots shown that are skewed left.
C. Z
D. Y
E. X
Stemplots
17. The stemplot below shows the ages of a garden club's members.
Member Age
2
3
4
5
6
7
8
9
036
15
2239
0000
2
Find the mean of the ages.
A. 54.8
B. 53
C. 52
D. 50.1
E. 47
Random Variables and Probability Distributions
18. Which of the following is a continuous random variable?
A. The number of windows in the White House.
B. The speed of a car.
C. The number of pages in a book.
D. The number of points scored in a basketball game.
E. The number of acorns on an oak tree.
Cumulative Frequency Plots
19. An organization is selling cookies to pay for a camping trip. Each member of the
organization is assigned boxes of cookies to sell over a 4 week period. The frequency table
below show the number of boxes sold by week.
Week
0-1 1-2 2-3 3-4
Frequency 200
500
300
500
Choose the ogive curve that represents the frequency table above.
W.
X.
Y.
Z.
A. Z
B. X
C. W
D. Y
E. The correct graph is not shown.
Surveys
20. A researcher wants to determine the percentage of high school students that drive and text
message in a particular state.
Which of the following methods would assure random selection of a sample population?
I) The researcher should randomly select one high school in the state and survey each student
enrolled.
II) The researcher should survey all high school students in the state.
III) The researcher should randomly select one high school in the state and survey randomly
selected students within the school.
IV) The researcher should randomly select a city in the state and survey all high school students
that reside within the city.
V) The researcher should randomly select students from all high school students that reside
within the state.
A. V
B. IV
C. III
D. II
E. I
Histograms
21. The histogram below shows the number of sales calls Adam conducted in a business day.
Which of the following is true?
A. The histogram is bimodal.
B. The histogram is symmetric.
C. The histogram has an outlier.
D. The histogram is contains a gap.
E. The histogram is multimodal.
The Normal Distribution
22. The amount 5th grade students grow during the school year is normally distributed with a
mean of 4 inches and a standard deviation of 1 inch. The amount 6th grade students grow during
the school year is normally distributed as well. They have a mean of 4 inches and a standard
deviation of 1 inch. Both distributions are shown below.
What percentage of 5th and 6th graders grow between 2 inches and 4 inches?
A. 49.7%
It is not possible to answer the question because it is not appropriate to use a normal
B.
distribution when there are two separate peaks.
C. 54.6%
D. 47.5%
The Normal Distribution
23. Intelligence quotient test scores are distributed normally and have a mean of 100 with a
standard deviation of 15. Calculate the z-score of a 110 IQ and round to the nearest hundredth.
A.
B.
C.
0.67
0.33
1.67
D. = 1
Stemplots
24. The stemplot below shows the ages of a garden club's members.
Member Age
2
3
4
5
6
7
8
Find the mode of the ages.
A. 52
B. 53
C. 50.1
D. 60
E. 82
9
036
15
2239
0000
2
Experiments
25. A company is conducting an experiment to test a new nutritional supplement. The company
randomly selects 2000 subjects. Half of the subjects are males, and the other half of the subjects
are females. The ages of the subjects range from 18 to 69.
The company creates pairs of males and pairs of females. One member from each individual pair
receives the nutritional supplement, while the other member receives a placebo.
Which of the following experimental designs describes the experiment above?
I)
II)
III)
IV)
Completely Randomized Design
Randomized Block Design
Matched Pairs Design
Randomized Pairs Design
A. IV
B. I
C. II
D. III
E. The design type is not listed.
Surveys
26. Lydia wants to conduct a survey regarding her high school's uniform policy. Which
technique would assure that Lydia's survey is well-designed and well-conducted?
Lydia should choose her closest friends to represent the entire student population. She
should then randomly select a group of her closest friends and administer the survey to her
A.
randomly selected friends.
Lydia should randomly select a sample of students from the entire student population. She
B. should then administer the survey to all of the randomly selected students.
Lydia should randomly select one class to represent the entire student population. She
C. should then administer the survey to all students in the randomly selected class.
Lydia should select one grade to represent the entire student population. She should then
randomly select students in the selected grade and administer the survey to the randomly
D.
selected students.
Lydia should randomly select one grade to represent the entire student population. She
E. should then administer the survey to all students in the randomly selected grade.
Data Collection
27. Janis enjoys making bread and wants to investigate the rate of mold growth on bread. She
makes bread dough and then the dough is divided into two even loaves. The loaves are then
baked and cooled equivalently. One loaf is then left on the counter, while the other loaf is placed
in a air tight container. Which of the following methods is being used to investigate the rate of
mold growth on the bread?
A. separation study
B. experimental study
C. observational study
D. controlled experiment
Box Plots
28. Which of the following box plots is symmetric?
W.
X.
Y.
Z.
A. Z
B. X
C. W
D. Y
E. There are no box plots shown that are symmetric.
Dotplots
29. The dotplot below shows the number of school sports and activities participated in by a
group of male students and a group of female students at Franklin High School.
Sport and Activity Participation
Male Students
* * * *
* * *
*
*
*
*
*
*
*
*
Female Students
0 * *
1
2
3 * * * * *
4 * * * * * * * *
Which of the following is true regarding the data set above?
I.
II.
The data set for male students possesses a gap.
The data set for female students possesses a gap.
III.
The mean of the male student data is less than the mean of the female student data.
IV.
The mean of the female student data is less than the mean
of the male student data.
A. II and III
B. I and IV
C. I and III
D. II and IV
E. III only
Random Variables and Probability Distributions
30. A research agency conducted a survey of 1,900 families, asking them how many children
they had. The following table lists the frequency distribution of the data collected.
Number of
Children
0
1
2
3
4
Number of
Families
38
437
1,045
228
152
What is the probability that a family chosen from this group at random will have 1 child?
A. 0.23
B. 0.25
C. 0.02
D. 0.98
E. 0.28
Categorical Data
31. The two-way frequency table below shows the extracurricular activities of juniors and
seniors at Franklin High School.
Extracurricular Activities
Band Athletics Drama Club Total
Male
90
180
45
315
Female
95
135
45
275
Total
185
315
90
590
Which of the following can be concluded from the marginal frequencies of the table above?
I.
The most popular extracurricular activity is athletics.
II.
There is more female involvement in extracurricular activities than male involvement.
III.
There is more male involvement in extracurricular activities than female involvement.
IV.
Drama club is the least popular extracurricular activity.
A. II and IV only
B. I, III, and IV
C. III and IV only
D. I, II, and IV
E. I and IV only
Dotplots
32. The dotplot below shows the number of books read over summer break by each student in
Mr. Smith's English class.
Number of Books Read
0 * *
1
2
3
4
*
*
*
*
* * *
* * * * * * * * *
* * *
*
Which of the following is true regarding the data set above?
I.
II.
III.
IV.
The data is skewed left.
The data is skewed right.
The data is symmetric.
The median of the data is 2.
A. I and IV
B. IV only
C. III only
D. III and IV
E. II and IV
Central Tendency and Spread
33. The frequency table shows the average number of hours Talia spends each week practicing
singing. What is the mode of the average hours?
WEEKLY AVERAGE HOURS OF
SINGING PRACTICE
Average Hours Frequency
A. 7 hours
B. 6 hours
C. 4 hours
D. 5 hours
4
2
5
5
6
4
7
7
8
2
Experiments
34. A drug company is testing a new influenza medicine. The company selects 100 adults, with
the same strain of influenza, to randomly form two groups: a control group and a treatment
group. The participants are unaware of their placements. The control group receives a placebo,
while the treatment group receives the influenza medicine. After 3 days, 25% of the control
group showed signs of improvement, even though they were only receiving a placebo.
Which of the following terms best explains the improvement in the control group?
A. placebo effect
B. bias
C. randomization
D. blinding
E. blocking
Surveys
35. A restaurant is conducting a survey regarding the quality of its food. The restaurant owner
prints a website on the bottom of all food receipts for an online survey.
State the type of bias that the survey presents.
A. nonresponse bias
B. the survey is not subject to bias
C. voluntary response bias
D. undercoverage
E. response bias
Probability
36. Ryan's mp3 player has 34 songs on it. There are 12 country songs, 10 rock songs, and 12 jazz
songs. If Ryan randomly selects 2 songs, without replacement, what is the probability that one
song will be country and one song will be rock?
A.
B.
C.
D.
E.
Independent and Dependent Variables
37. A contractor currently has 16 construction workers working on a building. When the building
is finished, it will have 20 stories. If he increases the number of workers to 32, the building will
be done twice as quickly. Which statement best describes the height of the building in this
situation?
A. The height of the building is the independent variable.
B. The height of the building is both an independent and a dependent variable.
C. The height of the building is the dependent variable.
D. The height of the building is neither an independent nor a dependent variable.
E. The height of the building is both an independent and a constant variable.
Data Collection
38. Which of the following would be the best method for investigating the wind speeds of
hurricanes?
A. questionnaire study
B. observational study
C. experimental study
D. survey
Categorical Data
39. A group of students were asked to choose their favorite sport. The results are shown in the
two-way frequency table below.
Favorite Sport
Football Baseball Basketball Soccer Total
Male
49
42
28
35
154
Female
14
21
28
49
112
Total
63
63
56
84
266
What percentage of females chose soccer as their favorite sport?
A. 13.16%
B. 18.42%
C. 22.73%
D. 43.75%
E. 31.58%
Cumulative Frequency Plots
40.
Jim and Bill each have a 6 month sales goal. The cumulative percentage plots above display the
monthly progress toward each employee's goal. Which of the following statements are true?
I.
II.
Jim and Bill both met their 6 month sales goal.
Jim met the median of his sales goal in the 3rd month, while Bill met the median of his
sales goal in the 2nd month.
III.
The greatest percentage of sales for Jim was in the 5th month.
IV.
The greatest percentage of sales for both Jim and Bill was in the 6th month.
A. I and II
B. II only
C. I only
D. IV only
E. I and III
Random Variables and Probability Distributions
41. A glass maker recycles 37% of the vases they make because of imperfections and their high
standards. If 8 vases are randomly chosen and inspected, what is the probability that 3 or 4 of
them will not pass inspection and be recycled?
A. 0.20667
B. 1.7829
C. 0.27146
D. 0.47813
E. 0.3003
Scatterplots
42. The weekly cost of groceries for a household is related to the number of people that reside in
the household. A collection of data on household size and the weekly cost of groceries of 10
households produced the scatterplot below.
Using the least squares method, write a linear regression equation that models the data above.
A.
B.
C.
D.
E.
Box Plots
43. A cell phone company conducted a survey regarding cell phone usage of high school
students. The company was specifically interested in the difference between male cell phone
usage and female cell phone usage. The cell phone company produced the box plots below to
show the number of cellular minutes that male and female students used in one month.
Cell Phone Usage
Which of the following statements are true regarding the box plots above?
I.
II.
About 50 percent of female students use 1000 to 1200 cellular minutes a month.
About 25 percent of male students use 300 to 400 cellular minutes a month.
III.
The median of female cell phone minute usage is greater than the median of male cell
phone usage.
IV.
The interquartile range of female cell phone minute usage is greater than the interquartile
range of male cell phone minute usage.
A. II and III
B. II and IV
C. I and IV
D. III and IV
E. I and III
Box Plots
44. The box plot below represents the finishing times, in seconds, of swimmers in a competition.
What percentage of swimmers completed the competition in 30 seconds or less?
Swimming Competition Finshing Times
Time (seconds)
A. 50 percent
B. 25 percent
C. 30 percent
D. 5 percent
E. 75 percent
Probability
45. Sam's closet contains blue and green shirts. He has eight blue shirts, and seven green shirts.
Five of the blue shirts have stripes, and four of the green shirts have stripes. What is the
probability that Sam randomly chooses a shirt that is blue or has stripes?
A.
B.
C.
D.
E.
Histograms
46. Timothy is conducting a study regarding adults and exercise. He surveyed a sample of adults
regarding their exercise habits, and he recorded his findings in the histogram below.
Which of the following are true?
I.
II.
III.
IV.
V.
This histogram is unimodal.
The histogram is bimodal.
The histogram is symmetric.
The histogram is skewed left.
The histogram is skewed right.
A. I only
B. II and III
C. II and V
D. II and IV
E. I and III
Scatterplots
47. Choose the scatterplot with positive correlation.
W.
X.
Y.
Z.
A. The correct graph is not shown.
B. X
C. Y
D. W
E. Z
Central Tendency and Spread
48. Retread is a used car lot where they line up the cars according to price. Today the front row
contains the following prices: $10,100, $6,400, $8,400, $8,700, $9,100, $10,100, and $9,100.
What is the median price in the front row?
A. $10,100
B. $8,900
C. $9,100
D. $8,843
Experiments
49. A bontanist is conducting an experiment to test a new fertilizer that has been developed for
roses. The bontanist has selected 800 experimental units. Half of the experimental units are red
roses, and the other half of the experimental units are white roses. All units are of equal maturity
levels.
The bontanist creates pairs of red roses and pairs of white roses. One plant in each individual pair
will receive fertilizer. The other plant in the pair will not receive any fertilizer.
Which of the following experimental designs describes the experiment above?
I)
II)
III)
IV)
A. I
B. III
C. II
Completely Randomized Design
Randomized Block Design
Matched Pairs Design
Randomized Pairs Design
D. The design type is not listed.
E. IV
Histograms
50. The histogram below shows a particular high school's enrollment.
Which of the following are true?
I.
II.
III.
IV.
V.
The histogram is unimodal.
The histogram is bimodal.
The histogram is multimodal.
The histogram has a uniform distribution.
The histogram is symmetric.
A. I and IV
B. V
C. III
D. IV and V
E. II and IV
Answers
1. B
2. A
3. A
4. D
5. A
6. D
7. B
8. B
9. D
10. D
11. B
12. B
13. A
14. D
15. A
16. C
17. D
18. B
19. C
20. A
21. D
22. D
23. A
24. D
25. D
26. B
27. D
28. C
29. A
30. A
31. B
32. D
33. A
34. A
35. D
36. A
37. D
38. B
39. D
40. A
41. D
42. A
43. A
44. B
45. B
46. B
47. E
48. C
49. B
50. D
Explanations
1. The category of the 4th month represents the total percentage of homes sold in the first 4
months. The question only asks for the percentage of homes sold in the 4th month. To find this
percentage, subtract.
Percentage of Homes Sold in
Month 4
Cumulative Percentage in Month 4 - Cumulative Percentage
in Month 3
= 80% - 50%
=
= 30%
In the 4 month, 30% of the homes were sold.
th
2. Mean
The mean of the data set can be found by adding all of the entries together and dividing by the
total number of entries.
Find the mean of the Tigers' scores.
(0 + 3 + 7 + 7 + 10 + 14 + 14 + 17 + 17 + 20 + 21 + 23 + 27 + 31 + 32 + 32) ÷ 16 =
275 ÷ 16
17.188
Find the mean of the Bears' scores.
(0 + 0 + 3 + 3 + 7 + 10 + 10 + 14 + 17 + 20 + 21 + 21 + 24 + 24 + 28 + 35) ÷ 16 =
237 ÷ 16
14.813
The mean of the Tigers' scores is greater than the mean of the Bears' scores.
Median
The median of an ordered data set is the middle value.
Find the median of the Tigers' scores.
17 + 17
2
= 17
Find the median of the Bears' scores.
14 + 17
2
= 15.5
The median of the Tigers' scores is greater than the median of the Bears' scores.
Range
The range of the data set is the difference between the largest and smallest values.
Find the range of the Tigers' scores.
Range of Tigers' Scores = 32 - 0
= 32
Find the range of the Bears' scores.
Range of Bears' Scores = 35 - 0
= 35
The range of the Tigers' scores is less than the range of the Bears' scores.
Given the information above, II and IV are both true statements.
3. Skewness
Skewness occurs when the entries of the data set are either distributed more to the left or more to
the right.
Most of the entries for the first competition lie to the right; therefore, the data set is said to be
skewed left.
Most of the entries for the second competition lie to the right; therefore, the data set is said to be
skewed left.
The first competition's distribution is skewed left, and the last competition's distribution is
skewed left.
Outlier
The outlier of a data set is the entry that varies greatly from the other entries in the data set. An
outlier typically lies at least 1.5 interquartile ranges below the first quartile or 1.5 interquartile
ranges above the third quartile.
In the first competition's data set, there is an outlier for the time interval of 30 to 60 seconds.
In the last competition's data set, there is not a value that lies at least 1.5 interquartile ranges
below the first quartile or 1.5 interquartile ranges above the third quartile; therefore, the data set
does not have an outlier.
The first competition's data set has an outlier.
Given the information above, both I and V are true statements.
4. In a controlled experiment, the researcher separates the sample population into groups with
one group designated as the control group.
All groups are manipulated in some way, except for the control group which remains the same.
5. A bar chart is a graph composed of bins, or equal-width columns. Each bin represents a
categorical variable, and the height of each bin represents the size of the category.
The heights of the bins in the bar chart displaying the monthly sales of Sam's Turkey sandwiches
are growing each month; therefore, it can be concluded that the sandwich is growing in
popularity.
The heights of the bins in the bar chart displaying the monthly sales of Sam's Ham sandwiches
are declining each month; therefore, it can be concluded that the sandwich is declining in
popularity.
Sam's Turkey sandwich grew in popularity, and Sam's Ham sandwich declined in
popularity.
6. Given that A and B are compound events, use the following conditional probability formula to
find the probability that event B will occur given that the event A has already occurred.
Define the events.
The question asks for the probability that a shirt has long sleeves given that the shirt is solid;
therefore, the formula for conditional probability must be applied.
Rewrite the formula for conditional probability for the given events, S and L.
Find P(S). Mark has 13 shirts, and 10 shirts are solid.
Find P(S
L). Mark has 13 shirts, and 6 of the shirts are solid and have long sleeves.
Substitute P(S) and P(S
obtain the final answer.
L) into the formula for conditional probability and simplify to
7. To find the mean, add the numbers together and divide by 8.
39.6 + 55.9 + 63.5 + 35.1 + 49.2 + 30.4 + 61 + 58.7 = 393.4
393.4 ÷ 8 = 49.175
The mean of this set of numbers is 49.175.
8. Skewness occurs when the entries of the data set are either distributed more to the left or more
to the right. In this case, most of the entries, lie to the left; therefore, the data set is said to be
skewed right. Given that the data set is skewed right, it can not be symmetric.
Gaps are areas of distribution with no observations. In this case, there is a gap in the ages of 40
and 50. The data set is, therefore, said to contain a gap.
Given the above information, both II and IV are true statements.
9. An independent variable is a variable whose value determines the value of other variables,
and it is changed in an experiment to see its effect on other variables.
A variable that changes because of a change in the independent variable is a dependent
variable.
In this situation, changing the number of construction workers changes the amount of time it will
take to complete the building.
Therefore, the time it takes to complete the building is the dependent variable in this
situation.
10. The mean of the data set can be found by adding all of the entries together and dividing by
the total number of entries. There are 26 total entries in this data set. Add all numbers together,
and divide by 26. The mean of the scholarship applications is 83 ÷ 26 = 3.2.
The range of the data set is the difference between the largest and smallest values. Find the
smallest number of scholarship applications, and subtract it from the largest number of
scholarship applications. The range of the scholarship applications is 7 - 0 = 7.
Symmetry occurs when the entries of the data set are equally distributed on both sides of the
median. In this case, the median of the data set is 2. It is seen that the other entries are not
equally distributed on the left and on the right of the median; therefore, the data set is not
symmetric.
Gaps are areas of distribution with no observations. In this case, there is a gap in the scholarship
application numbers of 4 and 5. The data set is, therefore, said to contain a gap.
Given the above information, only IV is a true statement.
11. The mean of the data set can be found by adding all of the entries together and dividing by
the total number of entries. Remember that each dot represents a single entry. There are 25 total
entries in this data set. Add all numbers together, and divide by 25.
65 ÷ 25 = 2.6
12. When given a normal distribution graph, the peak represents the mean of the data and the
following properties apply.



About 68% of the data lies within 1 standard deviation of the mean.
About 95% of the data lies within 2 standard deviations of the mean.
About 99.8% of the data lies within 3 standard deviations of the mean.
The following graph illustrates these properties.
From the answer choices, calculate the percentage of men who would fit if the height of the roof
was 36 in.
34% + 13.5% + 2.4% + 0.1% = 50%
Next, calculate the percentage of men who would fit if the height of the roof was 38.8 in.
13.5% + 34% + 34% + 13.5% + 2.4% + 0.1% = 97.5
Third, calculate the percentage of men who would fit if the height of the roof was 37.4 in.
34% + 34% + 13.5% + 2.4% + 0.1% = 84%
Finally, calculate the percentage of men who would fit if the height of the roof was 40.2 in.
2.4% + 13.5% + 34% + 34% + 13.5% + 2.4% + 0.1% = 99.9%
Therefore, in order for 99.9% of men to fit in the driver's seat, they must make the roof 40.2 in.
from the bottom of the seat.
13. An independent variable is a variable whose value determines the value of other variables,
and it is changed in an experiment to see its effect on other variables.
A variable that changes because of a change in the independent variable is a dependent
variable.
According to the statement in the question, a person's salary changes based on a change to the
number of years of education he or she has.
Therefore, the dependent variable in the statement is salary.
14. An influential point is a single point that strongly influences the slope and the intercept of a
regression model. If an influential point is removed from the data, the data will yield a very
different model.
The data points for Store A and Store B are the same except for one point. Store B has an
addition data point at 100o. The data point at 100o is called an influential point; therefore, it will
cause the model for Store B to differ than the model for Store A. In this case, the influential point
causes the model of Store B to have a greater slope than the model of Store A.
The models will have a different slopes and different intercepts because of th influential
point. Store A's slope will be less than Store B's slope.
15. To find the mean, first find the sum of the values in the set. Then divide the sum by the
number of values in the set.
Sum = $69 + $77 + $71 + $90 + $73 = $380
Mean = $380 ÷ 5 = $76
16. Skewness occurs when the entries of the data set are either distributed more to the left or
more to the right. In this case, the question asks for the box plot that is skewed left; therefore,
determine the box plot where most of the data lies to the right. The box plot that fits this
description is Z.
17. The mean of the data set can be found by adding all of the entries together and dividing by
the total number of entries. There are 15 total entries in this data set. Add all numbers together,
and divide by 15.
(29 + 30 + 33 + 36 + 41 + 45 + 52 + 52 + 53 + 59 + 60 + 60 + 60 + 60 + 82) ÷ 15 =
752 ÷ 15
50.133
18. A continuous random variable is a random variable that can assume any value in a given
interval. When this is the case, the number of possibilities can not be counted.
The number of acorns on an oak tree will always be a positive integer. Even though the number
is random, the number is countable. So, this is not a continuous variable.
The number of points scored in a basketball game will always be a positive integer. Even though
the number is random, the number is countable. So, this is not a continuous variable.
The number of pages in a book will always be a positive integer. Even though the number is
random, the number is countable. So, this is not a continuous variable.
There are an unchanging number of windows in the White House. So, it is not random. It is
always the same. So, this is not a random variable.
The speed of a car can take on the value of any real number in a large interval. So, this number
is both continuous and random. Therefore, this is a continuous random variable.
19. Find the cumulative frequencies.
Week
Frequency
Cumulative
Frequency
Find the cumulative percentages.
Week
Frequency
Cumulative
Frequency
Cumulative
Percentage
Plot the weeks and the associated cumulative percentages, using the upper bound for each week
category.
Connect the plotted points with a curve. The curve represents a continuous function.
The ogive curve that represents the frequency table is W.
20. The population being studied is all high school students residing in the state.
In order to assure random selection of a sample population, each high school student that resides
in the state must have an equal probability of being selected from the population. There is only
one method provided that will meet this criteria.
V) The researcher should randomly select students from all high school students that
reside within the state.
21. It is seen that Adam did not conduct any calls from 12:00 pm to 1 pm; therefore, the
histogram is said to contain a gap. Remember that gaps are areas of distribution with no
observations.
In order for a histogram to be bimodal or multimodal, the bins of the histogram must form two or
more peaks. Even though the given histogram appears to have two peaks, it only has one.
Remember that a peak is only formed when the frequency of a histogram changes from
increasing to decreasing.
Given the above information, the only true statement is that the histogram is contains a gap.
22. When given a normal distribution graph, the peak represents the mean of the data and the
following properties apply.



About 68% of the data lies within 1 standard deviation of the mean.
About 95% of the data lies within 2 standard deviations of the mean.
About 99.8% of the data lies within 3 standard deviations of the mean.
The following graph illustrates these properties.
Combining 5th and 6th grade growths will give the following.
Comparing this graph with the graph of percentages, calculate the percentage of 5th and 6th
graders who grow between 2 inches and 4 inches.
13.5% + 34% = 47.5%
Therefore, the percentage of 5th and 6th graders who grow between 2 inches and 4 inches is
47.5%.
23. Use the equation below to calculate the z-score of a 110 IQ where x represents the score to
convert,
Z=
represents the average IQ, and s is the standard deviation.
xs
110-100
=
15
10
=
=
15
0.6666...
0.67
24. The mode of an ordered data set is the entry seen most frequently. In this case, 60 is the only
value used four times, and four is the highest frequency found in the stemplot. The mode is 60.
25. There are three types of experiments.
Completely - The completely randomized design is the simplest form of experimental
Randomized design. In this design, all experimental units have an equal probability of
Design receiving any treatments available in the experiments.
Randomized - In this design, the experimental units are divided into blocks. Blocks are are
Block Design subgroups of similar experimental units. Each block is then randomized, and
all experimental units within each block have an equal probability of
receiving any treatments available in the experiments.
Matched Pairs - The matched pairs design is a special type of randomized block design. The
Design design can only be used when there are only two treatments available.
Subjects are divided into pairs based on a blocking variable, and each
experimental unit within the pair is then randomly assigned different
treatment options.
There is random selection with blocking in pairs in the given experiment; therefore, the
experiment follows the matched pairs design.
26. There are three characteristics that must be present in order to assure that a survey is welldesigned and well-conducted.
I)
A sample should be selected to survey. The selected sample should be an accurate
representation of the entire population of interest.
II) When the sample is selected, it must be randomized. Randomization assures that the sample
is an accurate representation of the entire population of interest, and it also reduces bias in
the survey.
III) When the sample is selected, it must be large enough. Selecting a sample size that is large
enough also assures that the sample is an accurate representation of the entire population of
interest.
In order for Lydia's survey to be well-designed and well-conducted, she must randomize. The
technique that properly assures randomization when selecting a sample to represent the
population is as follows:
Lydia should randomly select a sample of students from the entire student population. She
should then administer the survey to all of the randomly selected students.
27. In a controlled experiment, the researcher separates the sample population into groups with
one group designated as the control group.
All groups are manipulated in some way, except for the control group which remains the same.
28. Symmetry occurs when the entries of the data set are equally distributed on both sides of the
median. Determine the box plot where the data is equally distributed on both sides of the median.
The box plot that fits this description is W.
29. Gaps
Gaps are areas of distribution with no observations.
In the male students' data set, there is no gap or area of distribution without observations.
In the female students' data set, there is a gap in the participation of 1 sport/activity and 2
sports/activities. The data set is, therefore, said to contain a gap.
The data set for the female students possesses a gap.
Mean
The mean of the data set can be found by adding all of the entries together and dividing by the
total number of entries. Remember that each dot represents a single entry.
Find the mean of male students' participation. There are 15 total entries in this data set. Add all
numbers together, and divide by 15.
Mean of Male Students' Participation =
22 ÷ 15
1.467
Find the mean of female students' participation. There are 15 total entries in this data set. Add all
numbers together, and divide by 15.
Mean of Female Students' Participation =
47 ÷ 15
3.133
The mean of the male student data is less than the mean of the female student data.
Given the information above, II and III are both true statements.
30. To calculate the probability that a family chosen from this group at random will have 1 child,
divide the number of families that had 1 child by the total number of families surveyed.
31. When investigating the marginal frequencies of the extracurricular activities, it is seen that
athletics is the most popular activity and drama club is the least popular activity.
When investigating the marginal frequencies of the gender of students, it is seen that there is
slightly more male involvement than female involvement.
Given the information above, it is seen that I, III, and IV are all true.
32. Symmetry occurs when the entries of the data set are equally distributed on both sides of the
median. In this case, the median of the data set is 2. It is seen that the other entries are equally
distributed on the left and on the right of the median; therefore, the data set is said to be
symmetric. Given that the data set is symmetric, it can not be skewed.
Given the above information, both III and IV are true statements.
33. The mode is the number which occurs most often. The largest number in the frequency
column is 7, which corresponds with 7 hours.
A weekly average of 7 hours of singing practice occured 7 times, which is more often than any
other average.
Therefore, the mode is 7 hours.
34. The placebo effect occurs when 20% or more of experimental units show a positive response
to a placebo. The placebo effect often occurs when experimental units are human participants.
35. Bias is a failure to accurately represent a population in a sample or survey. There are four
types of bias.
Voluntary - Occurs when participation in a survey is determined by the individuals in
Response Bias the population, yielding a sample that is not an accurate representation of
the population
Nonresponse Bias - Occurs from a nonresponse to a survey, in which respondents' results
greatly differ from nonrespondents' results
Response Bias - Occurs from problems with the survey itself, specifically wording issues
Undercoverage - Occurs when members of a population are inadequately represented in a
sample population
The restaurant owner is not accounting for customers who do not have access to the internet;
therefore, undercoverage is present.
36. Given that A and B are compound events, use the following formula, defined as the
multiplication rule, to find the probability that A and B will occur. Remember that P(B|A) is the
probability that B will occur given that A has already occurred.
Note: Given that A and B are independent events, the multiplication rule will reduce to the
following formula.
Define the events.
The question asks for the probability that both events occur; therefore, the multiplication rule
must be applied.
Rewrite the multiplication rule for the given events, C and R.
Calculate P(C) and P(R|C).
Find P(C). There are 34 songs, and 12 of the total songs are country.
Find P(R|C). One song has already been selected; therefore, there are 33 songs remaining, and 10
of the total songs are rock.
Substitute P(C) and P(R|C) into the multiplication rule formula and simplify to obtain the final
answer.
37. An independent variable is a variable whose value determines the value of other variables,
and it is changed in an experiment to see its effect on other variables.
A variable that changes because of a change in the independent variable is a dependent
variable.
In this situation, changing the number of construction workers changes the amount of time it will
take to complete the building. However, the height of the building does not change at all.
Therefore, the height of the building is neither an independent nor a dependent variable.
38. In an observational study, the sample population is studied as is. The researcher does not
influence the population. Data is gathered and correlations are investigated.
In this situation, it is impossible to perform an experimental study or controlled experiment
because a hurricane cannot be artificially generated.
Of the choices given, the best way to investigate the correlation would be through an
observational study.
39. To calculate the percentage of females that chose soccer as their favorite sport, find the joint
frequency for the number of females that chose soccer. There are 49 females that chose soccer as
their favorite sport.
Find the marginal frequency for the total number of females. There are 112 females.
Calculate the percentage of females that chose soccer as their favorite sport.
40. To determine the distribution of the sales goals progresses, find the percentages of each
category by creating tables.
Create a table for Jim.
Jim's Sales Goal
Month
1
Percentage 10%
2
3
4
5
6
20% - 10% = 50% - 20% = 60% - 50% = 80% - 60% = 100% - 80% =
10%
30%
10%
20%
20%
The greatest percentage of sales for Jim was in the 3rd month.
Create a table for Bill.
Bill's Sales Goal
Month
1
Percentage 30%
2
3
4
5
6
50% - 30% = 70% - 50% = 80% - 70% = 90% - 80% = 100% - 90% =
20%
20%
10%
10%
10%
The greatest percentage of sales for Bill was in the 1st month.
The median of Jim's sales goal can be found by locating the bin with the cumulative height of 50
percent. In this case, the bin with the cumulative height of 50 percent is month 3; therefore, Jim
met the median of his sales goal in the 3rd month.
The median of Bill's sales goal can be found by locating the bin with the cumulative height of 50
percent. In this case, the bin with the cumulative height of 50 percent is month 2; therefore, Bill
met the median of his sales goal in the 2nd month.
The final bin of Jim's Sales Goal cumulative frequency plot has the height of 100, and the final
bin of Bill's Sales Goal cumulative frequency plot has the height of 100. Jim and Bill both met
their 6 month sales goal.
Given the information above, both I and II are true statements.
41. The situation given in the explanation represents a binomial probability distribution. The best
way to calculate the correct answer is to use the following binomial formula.
In this equation, n represents the total number of trials, p represents the probability of success, q
represents the probability of failure (1 - p), x represents the number of successes in n trials, and n
- x represents the number of failures in n trials. Now use this equation to find the probabilities for
when x = 3 and x = 4. Then add the probabilities to find the final answer.
42. The general form of the linear regression model is as follows.
Create a table of values for the household sizes (x) and weekly grocery costs (y) shown on the
scatterplot.
1
75
2
75
2
100
3
100
3
150
4
125
4
150
5
175
6
150
6
175
In order to solve for b0 and b1, find the mean of x, the mean of y, the standard deviation of x, the
standard deviation of y, and the correlation coefficient.
The mean of x and y can be found using the formulas below.
Using the formula above, find the mean of x.
Using the formula above, find the mean of y.
Find the standard deviation of x and y. The standard deviation of x and y can be found using the
following formulas.
Create a table for x-values to assist in the calculation of the standard deviation of x.
1
-2.6
6.76
2
-1.6
2.56
2
-1.6
2.56
3
-0.6
0.36
3
-0.6
0.36
4
0.4
0.16
4
0.4
0.16
5
1.4
1.96
6
2.4
5.76
6
2.4
5.76
Using the information in the table above and the formula for the standard deviation of x, find the
standard deviation of x.
Create a table for y-values to assist in the calculation of the standard deviation of y.
75
-52.5
2756.25
75
-52.5
2756.25
100
-27.5
756.25
100
-27.5
756.25
150
22.5
506.25
125
-2.5
6.25
150
22.5
506.25
175
47.5
2256.25
150
22.5
506.25
175
47.5
2256.25
Using the information in the table above and the formula for the standard deviation of y, find the
standard deviation of y.
Find the correlation coefficient. The correlation coefficient can be found by using the formula
below.
Create a table to find the product needed for the correlation coefficient.
-2.6
-52.5
136.5
-1.6
-52.5
84
-1.6
-27.5
44
-0.6
-27.5
16.5
-0.6
22.5
-13.5
0.4
-2.5
-1
0.4
22.5
9
1.4
47.5
66.5
2.4
22.5
54
2.4
47.5
114
Using the table above, the standard deviation of x, the standard deviation of y, and the formula
for the correlation coefficient, find the correlation coefficient.
Using the correlation coefficient, the standard deviation of x, the standard deviation of y, and the
formula for b1, calculate b1.
Using the mean of x, the mean of y, b1, and the formula for b0, find b0.
Substitute b0 and b1 into the general form of the linear regression model to obtain the final
answer.
The numbers found here may be slightly different than those found using a calculator due to
rounding.
43. The upper 25 percent of the female box plot is contained between 1000 to 1200; therefore,
about 25 percent of female students use 1000 to 1200 cellular minutes a month.
The lower 25 percent of the male box plot is contained between 300 to 400; therefore, about 25
percent of male students use 300 to 400 cellular minutes a month.
The median of the box plots are the middle values. The median number of cellular minutes used
by female students is 900, and the median number of cellular minutes used by male students is
500. The median of female cell phone minute usage is greater than the median of male cell
phone usage.
The interquartile range of each box plot can be found by subtracting the first quartile value from
the third quartile value for each box plot.
IQR of Female Students' Monthly Cell Phone Usage = 1000 - 800 = 200
IQR of Male Students' Monthly Cell Phone Usage = 700 - 400 = 300
The interquartile range of female cell phone minute usage is less than the interquartile
range of male cell phone minute usage.
Given the information above, statements II and III are true.
44. In this case, 30 forms the left side of the box; therefore, it represents the first quartile of the
data. Only about 25 percent of the data lies to the left of the first quartile.
Swimming Competition Finshing Times
Time (seconds)
Given the information above, it is seen that 25 percent of the swimmers completed the
competition in less than 30 seconds.
45. Given events A and B, use the following formula, defined as the addition rule, to find the
probability that A or B will occur.
Define the events.
The question asks for the probability that either event occurs; therefore, the addition rule must be
applied.
Rewrite the addition rule for the given events, B and S.
Calculate P(B), P(S), and P(B
S).
Find P(B). There are 15 total shirts in the closet, and 8 of the shirts are blue.
Find P(S). There are 15 total shirts in the closet, and 9 of the total shirts have stripes.
Find P(B
S). There are 15 total shirts in the closet, and there are 5 shirts that are blue and
have stripes.
Substitute P(B), P(S), and P(B
final answer.
S) into the addition rule formula and simplify to obtain the
46. Upon observation of the bins of the adults and exercise histogram, it is seen that the bins
form two peaks; therefore, the data is said to be bimodal. Given that the data set is bimodal, it
can not be unimodal or multimodal.
It is seen that the entries of the adults and exercise histogram are equally distributed on the left
and on the right of the median; therefore, the data set is said to be symmetric. Given that the data
set is symmetric, it can not be skewed.
Given the above information, both II and III are true.
47. A scatterplot with positive correlation is similar to a line with a positive slope. A scatterplot
with data running from the lower left of the plot to the upper right of the plot is said to have a
positive correlation; therefore, the answer is Z.
48. Arrange the numbers from smallest to largest; the median is the value in the middle of the
set, $9,100.
49. There are three types of experiments.
Completely - The completely randomized design is the simplest form of experimental
Randomized design. In this design, all experimental units have an equal probability of
Design receiving any treatments available in the experiments.
Randomized - In this design, the experimental units are divided into blocks. Blocks are are
Block Design subgroups of similar experimental units. Each block is then randomized, and
all experimental units within each block have an equal probability of
receiving any treatments available in the experiments.
Matched Pairs - The matched pairs design is a special type of randomized block design. The
Design design can only be used when there are only two treatments available.
Subjects are divided into pairs based on a blocking variable, and each
experimental unit within the pair is then randomly assigned different
treatment options.
There is random selection with blocking in pairs in the given experiment; therefore, the
experiment follows the matched pairs design.
50. It is seen that the entries of the school enrollment histogram are equally distributed on the left
and on the right of the median; therefore, the data set is said to be symmetric. Given that the
data set is symmetric, it can not be skewed.
It is also seen that the bins of the histogram are equal in height; therefore, the school enrollment
histogram is said have a uniform distribution. Given that the data set has a uniform
distribution, it does not have a mode; therefore, the data set can not be unimodal, bimodial, or
multimodal.
Given the above information, both IV and V are true.