Lesson 2 U2:
PRO
Probability
Sampling Analysis
1. Bill stood outside the mall and asked every fourth person to enter the
mall for their favorite sport. There were four choices: football, baseball,
basketball, and other. Bill surveyed a total of 54 people. Of those surveyed,
13 said football is their favorite, 14 said baseball is their favorite, 12 said
basketball is their favorite, and 15 said other.
Is there a sampling bias in the situation above?
A. Yes, people who go to the mall probably like baseball.
B. There is not enough information.
C. Yes, people who go to the mall probably like football.
D. No, there is no relationship between sports and going to the mall.
2. A store had 25 containers of trail mix on the shelf. Logan bought five
containers. The table below shows the number of pretzels in each of the
containers.
Sample of Trail Mix
Container Number of Pretzels
A
17
B
19
C
10
D
19
E
14
If the sample was representative of all 25 containers of trail mix, what was
the mode number of pretzels in each container of trail mix?
A. 17
B. 14
C. 19
D. 10
3. Amy is doing a science experiment on how a certain bacterium reacts to
an antibiotic. She has 3 dishes of identical bacterium samples with 11
bacteria in each dish. She gives an antibiotic to all of the bacteria in one
dish. All of the treated bacteria died, and the bacteria in the other two dishes
survived.
Identify the sample size in the situation above.
A. 3
B. 22
C. 33
D. 11
4. Amy is doing a science experiment on how a certain bacterium reacts to
an antibiotic. She has 3 dishes of identical bacterium samples with 17
bacteria in each dish. She gives an antibiotic to all of the bacteria in one
dish. All of the treated bacteria died, and the bacteria in the other two dishes
survived.
What type of sampling is demonstrated in the situation above?
A. convenience sampling
B. negative sampling
C. random sampling
D. census
5. Richard had a 550-piece puzzle with an image of a crossword puzzle. He
took out a handful of the pieces to examine, and found the following number
of letters on the pieces.
1, 3, 5, 5, 1, 3, 3, 5, 5, 1
Assuming that the sample was representative of the puzzle, what was the
mean number of letters on a piece of the puzzle?
A. 2
B. 3
C. 3.2
D. 5.3
6. Josh works for MooMoo Milkshakes. The company wants to know what
milkshake flavor is the most popular. Today, he surveyed every third female
customer on their favorite milkshake flavor. Twenty-two customers (out of
72 total) were surveyed, and 7 customers prefer MooChooChocolate, 4
customers prefer VeryStrawberry, and 11 customers prefer BananaBoBanna.
Identify the population in the situation above.
A. every female customer
B. every third female customer
C. MooMoo Milkshakes customers
D. every third customer
7. Josh works for MooMoo Milkshakes. The company wants to know what
milkshake flavor is the most popular. Today, he surveyed every third female
customer on their favorite milkshake flavor. Fifteen customers (out of 47
total) were surveyed, and 7 customers prefer MooChooChocolate, 4
customers prefer VeryStrawberry, and 4 customers prefer BananaBoBanna.
What type of sampling is demonstrated in the situation above?
A. random sampling
B. convenience sampling
C. census
D. negative sampling
8. During one month in the rainy season, a tropical forest received rain
every day. A scientist randomly picked seven days out of the month to
record the rainfall in inches. The amounts he picked are listed below.
4.2, 2.1, 2.7, 3.5, 2.1, 3.5, 2.1
If the sample was representative of the entire month, what was the mode of
the amounts of rainfall?
A. 2.7 inches
B. 3.5 inches
C. 2.1 inches
D. 2.89 inches
9. A street planner randomly selected 15 streets in the downtown area and
counted the number of parking meters on the street, as shown below.
57, 43, 52, 57, 61, 52, 61, 65, 43, 52, 61, 52, 65, 43, 52
Assuming that the sample was representative of all of the streets downtown,
what was the mode of the number of parking meters on a street?
A. 61
B. 52
C. 54.40
D. 43
10. Selma wants to know if seventh grade students prefer to do their math
homework in silence or with background music. She polled the 27 students
in her music class. Nine students preferred to do their math homework in
silence, and eighteen students preferred to do their math homework with
background music.
Identify the population in the situation above.
A. students who have math homework
B. students in Selma's music class
C. all seventh grade students
D. students who prefer to do math homework with background music
11. Three students from Milton Middle School are running for class
president. A preliminary poll was taken in three homeroom classes, each
with the same number of students. The results are shown in the table below.
Poll Results
Students Class A % Class B % Class C %
Ian
46
37
45
Jessie
27
29
9
Jeremy
27
34
46
Based on these preliminary results, who could be predicted to win class
president?
A. Ian
B. Jessie
C. Jeremy
D. cannot predict from these results
12. Selma wants to know if seventh grade students prefer to do their math
homework in silence or with background music. She polled the 24 students
in her music class. Eight students preferred to do their math homework in
silence, and sixteen students preferred to do their math homework with
background music.
Is there a sampling bias in the situation above?
A. No. Selma picked a completely random sample for her study.
B. Yes. Students in the music class will probably enjoy listening to music more than
other students.
C. Yes. Selma is only curious about 7th grade students, but 6th grade students may
prefer background music too.
D. There is not enough information.
13. Which of these is an example of a non-random sample?
A. Registered voters in Arizona are surveyed to determine if they have relatives in
Florida.
B. At a school assembly, five students are randomly chosen to receive free admission to
a theme park.
C. Airline passengers to Orlando, Florida, are asked about vacation plans.
D. Out of all the seventh grade students in a public school district, fifteen are chosen to
win a trip to a vacation destination.
14. The seventh grade class at a school had 255 students. The nurse called
in a random sample of 10 students to measure their heights in inches, as
shown below.
61, 52, 65, 67, 61, 51, 52, 51, 61, 65
If the sample was representative of the entire seventh grade, what was the
mode of the heights of the seventh grade class?
A. 61 inches
B. 58.6 inches
C. 56.5 inches
D. 56 inches
15. Josh works for MooMoo Milkshakes. The company wants to know what
milkshake flavor is the most popular. Today, he surveyed every third female
customer on their favorite milkshake flavor. Twenty-five customers (out of
83 total) were surveyed, and 7 customers prefer MooChooChocolate, 4
customers prefer VeryStrawberry, and 14 customers prefer BananaBoBanna.
Identify the sample size in the situation above.
A. 14
B. 7
C. 25
D. 83
16. Amy is doing a science experiment on how a certain bacterium reacts to
an antibiotic. She has 3 dishes of identical bacterium samples with 15
bacteria in each dish. She gives an antibiotic to all of the bacteria in one
dish. All of the treated bacteria died, and the bacteria in the other two dishes
survived.
Identify the sample in the situation above.
A. the antibiotic
B. all the bacteria in the treated dish
C. all bacteria everywhere
D. all the bacteria in all 3 dishes
17. In one day, 6,698 families visited a theme park. Tori asked eight
random families the amount that they spent and recorded the information in
the table below.
Theme Park Spending
Family Amount Spent ($)
1
228
2
119
3
178
4
228
5
88
6
228
7
88
8
178
Assuming that the sample was representative of the daily amount spent by
all the families, what was the approximate mean daily amount spent at the
park?
A. $158.14
B. $166.88
C. $103.50
D. $153.25
18. Selma wants to know if seventh grade students prefer to do their math
homework in silence or with background music. She polled the 27 students
in her music class. Nine students preferred to do their math homework in
silence, and eighteen students preferred to do their math homework with
background music.
What type of sampling is demonstrated in the situation above?
A. census
B. convenience sampling
C. random sampling
D. negative sampling
19. Amy is doing a science experiment on how a certain bacterium reacts to
an antibiotic. She has 3 dishes of identical bacterium samples with 19
bacteria in each dish. She gives an antibiotic to all of the bacteria in one
dish. All of the treated bacteria died, and the bacteria in the other two dishes
survived.
Is there a sampling bias in the situation above?
A. Yes. The antibiotic may not work on the other bacteria.
B. No. All 3 dishes are filled with the same number of identical bacteria.
C. There is not enough information.
D. Yes. The bacteria in the other 2 dishes are different than the treated bacteria.
20. Which of these is an example of a random sample?
A. The five people seated on the first row at the circus are asked their opinion about the
animal acts.
B. Henry asks five of his friends to fill out a survey to find out their favorite musicians.
C. The five employees who work the late shift answer questions about management.
D. Five employees out of 2,000 are chosen randomly to complete an anonymous survey.
21. On the opening day of a new movie, 244 people attended the premier.
The manager surveyed 8 random people as they left the theater. He asked
them to rate the movie on a scale of 1 to 10. Their ratings are below.
10, 1, 5, 10, 5, 8, 10, 8
Assuming that the sample was representative of the entire audience, what
was the mean rating of the movie for the entire audience?
A. 5.625
B. 8
C. 6
D. 7.125
22. Jim had a collection of 30 state quarters. He poured 10 of them onto the
table and noticed the years that the quarters were produced, as shown
below.
2005, 2006, 2008, 2003, 2001, 2001, 2006, 2006, 2005, 2003
Assuming that the sample was representative of the collection, what was the
mode of the year that the quarters were produced?
A. 2001
B. 2008
C. 2005
D. 2006
23. Bill stood outside the mall and asked every fourth person to enter the
mall for their favorite sport. There were four choices: football, baseball,
basketball, and other. Bill surveyed a total of 50 people. Of those surveyed,
14 said football is their favorite, 12 said baseball is their favorite, 11 said
basketball is their favorite, and 13 said other.
Identify the population in the situation above.
A. everyone who likes basketball
B. everyone entering the mall
C. every fourth person to enter the mall
D. everyone who likes baseball
24. A professional basketball player participated in 1,394 games in his
career. He randomly chose eight games to determine the number of points
he made per game, as shown below.
28, 17, 29, 17, 24, 28, 24, 28
If the sample was representative of his entire career, what was the mode of
the number of points per game?
A. 24.375
B. 28
C. 26
D. 20.5
25. A travel agency created a pamphlet for a city. They chose the high
temperature for 10 random days during the year to calculate the
temperature for the entire year, as shown below.
68°F, 76°F, 84°F, 60°F, 84°F, 68°F, 76°F, 68°F, 84°F, 60°F
Assuming that the sample was representative of the daily temperature for
the entire year, what was the mean daily temperature?
A. 72°F
B. 76°F
C. 72.8°F
D. 66°F
26. An airplane company flies 35 airplanes daily. The CEO collects the
following passenger counts for a random sample of airplanes from the fleet,
as shown below.
111, 147, 151, 82, 151, 111, 147, 111, 151, 82
Assuming that the sample is representative of the entire fleet of airplanes,
what would be the mean daily passenger count per plane?
A. 124.4
B. 122.75
C. 129
D. 132.6
27. Which of these is an example of a random sample?
A. At a team owners meeting, three people are surveyed to determine the percent of the
population who enjoy basketball.
B. One of the three best basketball players on a team are randomly chosen for a
basketball shoot-out.
C. Three audience members are randomly chosen to participate in a halftime shoot-out
at a basketball game.
D. A sports store asks customers whether or not they enjoy basketball.
28. Selma wants to know if seventh grade students prefer to do their math
homework in silence or with background music. She polled the 27 students
in her music class. Nine students preferred to do their math homework in
silence, and eighteen students preferred to do their math homework with
background music.
Identify the sample size in the situation above.
A. There is not enough information.
B. 18
C. 27
D. 9
29. A circus had 36 performances in one year. The entertainment company
which owned the circus analyzed sales receipts for 12 of the performances
and recorded the following number of t-shirt sales.
827, 685, 854, 742, 827, 792, 854, 685, 854, 742, 827, 854
Assuming that the sample was representative of all of the performances,
what was the mode of the number of t-shirts sold at a performance?
A. 823
B. 795.25
C. 827
D. 854
30. Janet wanted to determine her average phone call length over 90 days.
She collected the phone bills and randomly picked ten entries to look at. The
phone call lengths, in minutes, are shown below.
3, 7, 16, 7, 13, 3, 13, 3, 16, 3
Assuming that the sample was representative of all the entries on the bills,
what was the mean number of minutes over 90 days?
A. 9.75
B. 8.4
C. 7
D. 7.7
31. Selma wants to know if seventh grade students prefer to do their math
homework in silence or with background music. She polled the 30 students
in her music class. Ten students preferred to do their math homework in
silence, and twenty students preferred to do their math homework with
background music.
Identify the sample in the situation above.
A. students who prefer to do math homework with background music
B. students in Selma's music class
C. students who have math homework
D. all seventh grade students
32. A botanist grew a variety of hibiscus with spots on the petals. Below is a
list of the number of spots on a random sample of flowers.
7, 12, 4, 12, 7, 9, 5, 5, 7, 5, 5
Assuming that the sample was representative of all of the flowers, what was
the mode of the number of spots on a flower?
A. 5
B. 9
C. 7.09
D. 7
33. A movie theater conducted a survey to see what customers preferred at
the concession stand. The theater asked every fifth person who entered the
movie theater every Friday for a month what his or her favorite movie snack
was. Were the results of the survey valid?
A. No, because the theater did not use a random sample.
B. No, because the theater did not survey everyone in the theater.
C. Yes, because the theater only surveyed children.
D. Yes, because the theater surveyed a random sample.
34. Bill stood outside the mall and asked every fourth person to enter the
mall for their favorite sport. There were four choices: football, baseball,
basketball, and other. Bill surveyed a total of 53 people. Of those surveyed,
15 said football is their favorite, 13 said baseball is their favorite, 13 said
basketball is their favorite, and 12 said other.
Identify the sample size in the situation above.
A. 66
B. 53
C. 26
D. 41
35. A warehouse had 930 bags of flour. A health inspector randomly chose
15 of the bags and found the following number of weevils in them.
25, 20, 28, 20, 32, 25, 20, 34, 32, 25, 20, 34, 28, 20, 28
Assuming that the sample was representative of all of the bags in the
warehouse, what was the mode of the number of weevils in a bag?
A. 26.07
B. 34
C. 25
D. 20
36. Josh works for MooMoo Milkshakes. The company wants to know what
milkshake flavor is the most popular. Today, he surveyed every third female
customer on their favorite milkshake flavor. Twenty-four customers (out of
77 total) were surveyed, and 7 customers prefer MooChooChocolate, 4
customers prefer VeryStrawberry, and 13 customers prefer BananaBoBanna.
Identify the sample in the situation above.
A. today's MooMoo Milkshakes customers
B. every third female customer
C. every third customer
D. every female customer
37. Bill stood outside the mall and asked every fourth person to enter the
mall for their favorite sport. There were four choices: football, baseball,
basketball, and other. Bill surveyed a total of 47 people. Of those surveyed,
13 said football is their favorite, 11 said baseball is their favorite, 12 said
basketball is their favorite, and 11 said other.
Identify the sample in the situation above.
A. every fourth person entering the mall
B. everyone entering the mall
C. everyone who likes football
D. everyone who likes basketball
38. A restaurant has 46 main dishes on their menu and lists the calorie
count for each. The calories for the dishes that five friends randomly choose
from the menu are listed below.
Menu Items
Dish
Fish Burger
Number of Calories
1,338
Chicken Blaze
1,467
Dessert for Dinner
1,217
Beef Lasagna
1,338
Cheese Bliss
1,501
Assuming that the sample is representative of the entire menu, what is the
mean number of calories per main dish?
A. 1,338.5
B. 1,402.5
C. 1,380.75
D. 1,372.2
39. The produce manager was trying to regulate the number of grapes
placed in each of the produce bags. He took a random sample of 9 bags and
counted the number of grapes. The counts are listed below.
153, 166, 137, 147, 170, 147, 166, 153, 147
If the sample was representative of all the produce bags, and there were 36
bags, what was the mode of the number of grapes per bag?
A. 154.00
B. 153
C. 147
D. 154.88
40. Which of these is an example of a non-random sample?
A. Ten college students at a college, population 50,000, are chosen to taste test a new
cereal.
B. A farmer is choosing grains of wheat from a field to test for a new flavor of cereal.
C. A cereal company puts a winning ticket in one box of cereal out of 100,000 boxes.
D. A cereal company surveys their employees about breakfast food preference.
41. Which of these is an example of a random sample?
A. Every twentieth caller to an independent radio station receives tickets to a concert.
B. Customers buying a new cell phone are surveyed about cell phone plans.
C. A phone plan company surveys people on the beach to see how well they are
receiving service, and uses this information in future advertising.
D. A phone survey is conducted using twenty names randomly taken from the phone
book.
42. The CEO of a company wanted to know how many cups of coffee his
employees drank in a week. The number of cups of coffee drank by ten
people are shown below.
5, 12, 3, 12, 5, 9, 5, 12, 12, 9
Assuming that the sample was representative of the entire company, what
was the mean number of cups of coffee drank per week by an employee in
the company?
A. 8.4
B. 7.15
C. 12.5
D. 6.375
43. A book had 220 pages. Liliana wanted to estimate the number of words
per page, so she counted the words on 10 random pages. The word counts
are listed below.
145, 158, 173, 119, 173, 145, 158, 145, 173, 119
Assuming that the sample was representative of the entire book, what was
the mean number of words per page?
A. 145
B. 150.8
C. 162.7
D. 119
44. A city council conducted a survey on speed bumps to see what residents
preferred. The council asked every resident in one particular neighborhood
what his or her preferences were. Were the results of the city council's
survey valid?
A. No, because neighborhoods do not have speed bumps.
B. Yes, because every resident in a neighborhood was surveyed.
C. No, because the sample was not random.
D. Yes, because the neighborhood surveyed wanted speed bumps.
45. Bill stood outside the mall and asked every fourth person to enter the
mall for their favorite sport. There were four choices: football, baseball,
basketball, and other. Bill surveyed a total of 50 people. Of those surveyed,
12 said football is their favorite, 14 said baseball is their favorite, 11 said
basketball is their favorite, and 13 said other.
What type of sampling is demonstrated in the situation above?
A. census
B. random sampling
C. negative sampling
D. convenience sampling
46. Josh works for MooMoo Milkshakes. The company wants to know what
milkshake flavor is the most popular. Today, he surveyed every third female
customer on their favorite milkshake flavor. Twenty-one customers (out of
67 total) were surveyed, and 8 customers prefer MooChooChocolate, 4
customers prefer VeryStrawberry, and 9 customers prefer BananaBoBanna.
Is there a sampling bias in the situation above?
A. There is not enough information.
B. Yes. Josh only asked female customers.
C. No. The company is only interested in males' opinions.
D. No. Josh asked random customers, so there is no bias.
47. Amy is doing a science experiment on how a certain bacterium reacts to
an antibiotic. She has 3 dishes of identical bacterium samples with 15
bacteria in each dish. She gives an antibiotic to all of the bacteria in one
dish. All of the treated bacteria died, and the bacteria in the other two dishes
survived.
Identify the population in the situation above.
A. all the bacteria in all 3 dishes
B. the antibiotic
C. all the bacteria in the treated dish
D. all bacteria everywhere
48. A company was trying to decide how to buy health care for their
employees. They surveyed a random sample of 10 employees and asked
them to select the monthly premium they would pay for a select set of
benefits. The amounts they were willing to pay are listed below.
$154, $119, $141, $206, $154, $141, $119, $119, $183, $119
If the sample was representative of the entire company, and the company
has 137 employees, what was the mode of the amount that all of the
employees were willing to pay?
A. $183
B. $206
C. $119
D. $141
49. The venue for an outdoor summer concert was divided into 35 sections.
The event planner randomly chose 8 sections and counted the number of ice
chests in the section, as shown below.
39, 50, 30, 66, 50, 39, 30, 50
Assuming that the sample was representative of the entire venue, what was
the mean number of ice chests in a section?
A. 44.25
B. 44.5
C. 50
D. 46.25
50. The school district designed a district wide end-of-course exam for
math. Last year, 336 students took the exam. A random sample of exam
scores, shown below, were chosen to represent the entire group.
88, 95, 61, 88, 61, 88, 77, 95, 95, 68, 77, 95, 77, 77, 61, 88
Assuming that the sample was representative of all of the exam scores, what
was the mean exam score for all the end-of-course exams?
A. 81.125
B. 80.6875
C. 77
D. 77.8
51. For a lesson on statistics, the students in a math class counted the
number of yellow candies in 10 individual candy bags out of a box of 75
bags. The data is shown below.
17, 10, 10, 14, 18, 10, 14, 18, 17, 10
If the sample was representative of all 75 bags, what was the mode number
of yellow candies for the entire box?
A. 17
B. 10
C. 14
D. 18
52. An environmentalist was investigating the impact of a chemical spill on
the minnow population in a lake. He randomly caught and released 16
minnows, counting the number of missing scales on the fish, as shown
below.
4, 3, 11, 4, 9, 7, 9, 11, 4, 3, 4, 7, 9, 11, 7, 4
Assuming that the sample was representative of the entire population in the
lake, what was the mean number of missing scales on a minnow?
A. 6.8
B. 7.375
C. 7.5
D. 6.6875
53. Three different clothing stores in different parts of a city recorded the
number of swimsuits they sold for four months.
Swimsuit Sales
Month # Sold
Month # Sold
Month # Sold
June
239
June
289
June
212
July
224
July
241
July
249
Aug
189
Aug
174
Aug
196
Sept
157
Sept
105
Sept
152
Based on these results, how many swimsuits should clothing stores in the
same city predict to sell in October?
A. more swimsuits than September
B. less swimsuits than September
C. the same number of swimsuits as September
D. cannot predict from these results
54. A national pizza chain collected data from 150 stores about pizza orders
on a busy Saturday. The number of pizzas ordered from 15 random stores is
below.
23, 56, 36, 61, 36, 23, 61, 41, 56, 56, 61, 56, 61, 61, 36
If the sample was representative of the entire chain, what was the mode of
the number of pizzas ordered for all 150 stores?
A. 41
B. 61
C. 56
D. 48.27