# Identify the letter of the choice that best completes

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```					Exam Review

Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.

____    1. A broken-line graph is best used to describe
a. the frequency of a data category              c. the spread of data
b. trends of the data over time                  d. the percentage of data in each category
____    2. Samantha surveys the students in her class and finds that the average math mark of females is higher than that
of males. She concludes that females are better in math than males. Samantha's study is flawed because
a. she did not ask for the students' marks in other courses
b. her sample size was not large enough
c. she did not say how much higher was the females’ average mark
d. she did not draw a graph
____    3. In the following graph, what type of correlation is indicated?

a. strong positive                                c. weak positive
b. strong negative                                d. weak negative
____    4. An agricultural researcher wishes to study how the price of a new type of crop being grown in 10 counties
across the country will vary with the weather. What type of study will be the most appropriate?
a. cross-sectional study that uses a sample of the counties where the crop is grown
b. cross-sectional study that takes a census of the counties where the crop is grown
c. longitudinal study that uses a sample of the counties where the crop is grown
d. longitudinal study that takes a census of the counties where the crop is grown
____    5. In which scenario is it better to take a sample rather than a census?
a. testing light bulbs being manufactured in a plant to see how long they last
b. determining the termite population in a city
c. both a and b
d. neither a nor b
____   6. In a secondary school, there are 5 classes of grade 9 academic mathematics. The classes are labelled A, B, C,
D, and E. Each class has 30 students. In each class, the students are numbered from 1 to 30. The label A06
indicates the sixth student in class A. A random sample of 10 students enrolled in grade 9 academic
mathematics at this school results in the following students being selected:

A05,      A20,      B05,      B20,        C05,    C20,        D05,    D20,      E05,      E20

Which sampling method could not have been used?
a. simple random sampling                        c. cluster sampling
b. stratified sampling                           d. systematic random sampling
____   7. In a secondary school, there are 5 classes of grade 9 academic mathematics. The classes are labelled A, B, C,
D, and E. Each class has 30 students. In each class, the students are numbered from 1 to 30. The label A06
indicates the sixth student in class A. A random sample of 10 students enrolled in grade 9 academic
mathematics at this school results in the following students being selected:

A01,      A03,      A09,      A12,        A19,    A21,        A23,    A24,      A29,      A30

Which sampling method might have been used?
a. simple random sampling
b. multi-stage random sampling
c. either simple or multi-stage random sampling
d. neither simple nor multi-stage random sampling
____   8.   A magazine conducts an annual survey of its subscribers. One year it takes a random sample of 100 of its
subscribers and contacts them by telephone. If there is no answer, the subscriber is called back until a
response is obtained. The next year it puts a survey in all copies of the magazine. The survey is mailed to
subscribers and 1200 are completed and returned. Which of the following best describes the bias that results
from these two sampling methods?
a. the first is more biased since fewer people are surveyed
b. the first is less biased since it is based on a random sample
c. both methods suffer from bias
d. neither method will lead to biased results
____   9.   A histogram has a bin width of 0.5. The left end point of the first interval is 7.25. What is the left end point of
the sixth interval?
a. 9.75                                             c. 12.25
b. 10.25                                            d. 13.25
____ 10.    The median mass of a collection of 8 oranges, some of which have the same mass, is 200 g. If a ninth orange
heavier than all the others is added to the collection, what effect will it have on the median?
a. cannot be determined                             c. it will be unchanged
b. it will increase                                 d. it will decrease
____ 11.    Sam observed that after one positive number in a certain data set was changed to zero only one of the mean,
median, and mode changed. Which one was it?
a. cannot be determined                             c. median
b. mean                                             d. mode
____ 12.    Find the first quartile for the numbers of children in twenty families:

Number of Children             0      1      2     3      4      5
Frequency                      1      4      7     5      1      2

a. 1                                              c. 2
b. 1.5                                            d. 2.5
____ 13.   The masses of 500 boxes of sugar are approximately normally distributed with a mean of 150g and a standard
deviation of 3g. How many of these boxes would you expect to have a mass greater than 150g?
a. 250                                            c. 256
b. 253                                            d. 259
____ 14.   Find the percentile corresponding to x = 15 if X~N(12, 2.62).
a. 12th                                           c. 87th
b. 13th                                           d. 88th
____ 15.   Namdar’s BMI is 32.87. What is his mass, to the nearest kilogram, if he is 170 cm tall?
a. 55                                             c. 94
b. 56                                             d. 95
____ 16.   Three percent of the lightbulbs produced by a company are defective. A simulation using a spreadsheet is
conducted to determine the probability that four out of the next eleven lightbulbs produced are defective. This
simulation is run 58 times, with each row in the spreadsheet simulating a trial. The entries in the spreadsheet
could be the numbers
a. 1 to 58                                        c. 1 to 10
b. 1 to 100                                       d. none of the above
____ 17.   In a hat, there are 2 nickels and 2 dimes. If two coins are chosen at random at the same time, the probability
that both are nickels is
a.                                                c.

b.                                              d.

____ 18. A pair of students is picked randomly from four students John, Sara, Adam, and Laura. Determine the
probability that a girl will be chosen given that Adam has been chosen already.
a.                                                c.

b.                                              d.

____ 19. Identify which situation represents two dependent events.
a. drawing two cards from a deck without replacement
b. flipping a coin twice
c. rolling a pair of dice one after the other
d. none of the above
____ 20. A coin is flipped and a card drawn from a regular deck of cards. Determine the probability of drawing an ace
given that the flip is heads.
a.                                              c.

b.                                              d.

____ 21. Determine the number of ways that a prime minister, secretary, treasurer, and publicity minister could be
chosen from an art club of 12 members.
a. 495                                          c. 11 880
b. 48                                           d. 20 736
____ 22. Three cards are drawn randomly from a hat containing cards with the twenty-six letters of the alphabet on
them. Determine the probability of selecting A and B.
a.                                               c.

b.                                               d.

____ 23. Determine the probability of choosing the jack and king of clubs out of a regular deck of cards when two
cards are randomly chosen.
a.                                              c.

b.                                               d.

____ 24. A game is played by spinning a wheel that is divided into four sectors, each with a different point value. The
central angle and point value for each sector is shown in the chart below.
Central Angle       Point Value
144°                  20
108°                  30
72°                  40
36°                  50

How many total points would you expect to get for 100 spins of the wheel?
a. 3500                                         c. 2500
b. 3000                                         d. 2000
____ 25. The following table shows the probability distribution for the possible sums that result from rolling two 6-
sided dice.

X            P(X)             X           P(X)
1             0               7

2                             8

3                             9

4                            10

5                            11

6                            12

What is the probability that the sum rolled is even and less than 9?
a.                                               c.

b.                                               d.
____ 26. What is the probability of drawing exactly 2 red cards in a hand of 3 cards drawn from a deck of 52 cards?
a.                                              c.

b.                                               d.

____ 27. If                                               , what is the value of n?

a. 6                                               c. 4
b. 8                                               d. 5
____ 28. A baseball player hits the ball to left field 20% of the time, to centre field 35% of the time, and to right field
45% of the time. Which of the following expressions gives the probability distribution for the number of hits
to centre field for a game in which the batter gets 5 hits?
a.                                                 c.

b.                                               d.

____ 29. The probability of a computer memory chip being defective is 0.02. Which of the following statements is
true?
a. In a shipment of 100 chips, two will be defective.
b. The expected number of defective chips in a shipment of 500 is ten.
c. In a shipment of 1000 chips, it is certain that at least one will be defective.
d. All statements above are false.
____ 30. A Bernoulli trial has a probability of success of 0.4. What is the smallest number of trials for which a normal
distribution can be used to approximate its probability distribution?
a. 12.5                                           c. 10
b. 20                                             d. 13

31. What sampling method is being used in the following scenario? In order to assess the impact of acid rain on a
northern lake, a randomly chosen day of the week is selected. Then water samples from the lake are collected
on that day every week for a year.
32. Where is the interval with greatest frequency located in a histogram that has a mound-shaped distribution.
33. State the measure of central tendency that is most appropriate to describe the ages of these five starters on a
basketball team: 24, 22, 39, 22, 23.
34. The table below lists the heights in centimetres of all of the teachers in a school. Find the modal interval.

Height (cm)       150–159        160–169        170–179          180–189         190–199
Frequency            6             10             20                18              4
35. The median annual salary of the 6 vice-presidents of AVCO Inc. is \$150 000. What will this median be if
only the highest paid vice-president receives a \$50 000 raise?
36. A set of numbers has Q2 = 22 and Q3 = 73. What would the values of these be if all of the numbers in the set
were decreased by 7?
37. A CD is defective 3% of the time. A simulation is done by a spreadsheet which produces random numbers
from 1 to 100. What are the possible numbers that represent a non-defective CD?
38. A spinner is divided into 21 equal sectors, numbered 1 through 21. Determine the probability of spinning a
number other than an even number.
39. The probability of rolling a two on a die is to be determined. State the value of               .
40. Determine the probability of rolling snake eyes (2 ones) with a pair of dice.
41. A spinner with three equal sections labelled A, B, and C is spun. Determine the probability that the spinner
lands on A or B at least once.
42.   A family has four children. Determine the probability that the first and third children are boys.

43. Solve for    if                .

44. If                , determine the odds of event   occurring.

45. Draw a chart to show the probability distribution for all the sums of two four-sided dice.

46. Use Pascal’s Identity to write an expression equivalent to         .

47. Write the terms in the unsimplified expansion of               .
48. How many paths are possible from the marked point A to the lowest point B if you are allowed to move down
to either the right or left?

A

B
49. A manufacturer of halogen bulbs knows that 3% of the production of their 100 W bulbs will be defective.
What is the probability that exactly 5 bulbs in a carton of 144 bulbs will be defective?
50. Compare the standard deviation for the normal approximation to a binomial experiment with p = 0.43 for 100
trials and 400 trials.

Problem

51. Describe how to obtain a simple random sample of 5 households from a population of 60 000 households.
52. Explain how cluster sampling and stratified sampling both use simple random samples as part of the sampling
process.
53. A nutritionist promoting healthy eating practices wants to conduct a survey. The survey is to determine the
average amount of fat consumed per day by adults in a city. Because members of any one family eat mostly
the same meals, she will only interview at most one adult per household and wants to survey 1000 people.
She has no list of the individual people in the city, but she has a map showing the housing for each block in
detail. Identify the population, the sample, the variables to be measured, and the most appropriate sampling
method.
54. An experiment is to be conducted that compares different diets for patients with Type II diabetes. Patients are
randomly selected to follow one of three diets and are counselled about the types of foods that should be
eaten. Explain why it is impossible to conduct this as a double-blind experiment.
55. A large study is to be conducted to determine if taking aspirin reduces the risk of having a heart attack.
Approximately 10 000 participants took an aspirin every other day, while 10 000 participants took a pill that
looked and tasted like aspirin but had no active ingredients. Neither the participants nor the attending doctors
knew which type of pill was being taken by each participant. For this experiment, identify the treatment
group, the control group, the placebo, if any, and whether or not the experiment is double-blind.
56. The mean of Tanya’s marks on five tests was 77.4. The marks on the first 4 of these tests were 88, 77, 70, and
72. Find the mark on the fifth test.
57. Fred was told by his teacher that the mean final mark of all the students in his class was exactly 68.7. He
surveyed these students and recorded the results in a frequency table with intervals 1–10, 11–20, et cetera.
Will his calculated mean equal the one calculated by his teacher?
58. “If all the numbers in a data set are squared then the median will also be squared.” Prove this statement or
give a counterexample which is an example that shows the statement is false in general.
59. When is the standard deviation larger than the variance? Explain with an example.
60. A group of 200 candidates apply for a job. Only 10 will be given interviews and only 3 of those candidates
will be given second interviews. If the selection process is completely random, what is the probability of
being given a second interview?
61. Create a survey that uses a probability question where the probability of a second event happening given a

first event happening is   and the probability of the first event happening is . Tally the results in a chart.

62. Solve for n if P(n, 5) = 120C(n, 3).
63. It is said that a sports team can gain confidence if it wins games and can lose confidence if it loses games.
Explain how the formula for conditional probability applies when determining the probability of a team
winning its next two games, given that it has a 50% chance of winning the first game. State what this
probability must be greater than given this theory of confidence.

64. Use the Binomial Theorem to simplify the expansion of                  .

65. A student writes a five question multiple-choice quiz. Each question has four possible responses. The student
guesses at random for each question. Calculate the probability for each possible score on the test from 0 to 5.
66. Two four-sided dice are rolled and the sum observed is recorded.
a) List the possible outcomes for the two dice and the resulting sums.
b) Create a table showing the probability distribution of the random variable representing the sum observed.
c) Calculate the expected value for the sum observed.
67. Explain the difference between a discrete and a continuous variable and how this concept is important in the
procedure of finding the normal approximation to a binomial distribution.
Exam Review

MULTIPLE CHOICE

1. ANS: B              REF: Knowledge and Understanding        OBJ: 1.1 Visual Displays of Data
LOC: DMV.01         TOP: The Power of Information
2. ANS: B              REF: Knowledge and Understanding        OBJ: 1.2 Conclusions and Issues
LOC: ST5.02         TOP: The Power of Information
3. ANS: C              REF: Knowledge and Understanding        OBJ: 1.3 The Power of Visualizing Data
LOC: ST4.03         TOP: The Power of Information
4. ANS: D              REF: Application OBJ: 2.2 Characteristics of Data
LOC: ST1.01         TOP: In Search of Good Data
5. ANS: C              REF: Knowledge and Understanding        OBJ: 2.2 Characteristics of Data
LOC: STV.01         TOP: In Search of Good Data
6. ANS: C              REF: Knowledge and Understanding        OBJ: 2.3 Collecting Samples
LOC: DMV.01, STV.01, ST1.01              TOP: In Search of Good Data
7. ANS: C              REF: Knowledge and Understanding        OBJ: 2.3 Collecting Samples
LOC: DMV.01, STV.01, ST1.01              TOP: In Search of Good Data
8. ANS: B              REF: Knowledge and Understanding        OBJ: 2.5 Avoiding Bias
LOC: ST1.02, ST1.03, ST5.02              TOP: In Search of Good Data
9. ANS: A              REF: Knowledge and Understanding
OBJ: 3.1 Graphical Displays of Information                  LOC: STV.02
TOP: Tools for Analyzing Data
10. ANS: A              REF: Application OBJ: 3.2 Measures of Central Tendency
LOC: ST2.01         TOP: Tools for Analyzing Data
11. ANS: B              REF: Application OBJ: 3.2 Measures of Central Tendency
LOC: ST2.01         TOP: Tools for Analyzing Data
12. ANS: B              REF: Knowledge and Understanding        OBJ: 3.3 Measures of Spread
LOC: ST2.01         TOP: Tools for Analyzing Data
13. ANS: A              REF: Knowledge and Understanding        OBJ: 3.4 Normal Distribution
LOC: ST3.02         TOP: Tools for Analyzing Data
14. ANS: C              REF: Knowledge and Understanding
OBJ: 3.5 Applying the Normal Distribution: Z-Scores         LOC: ST2.03
TOP: Tools for Analyzing Data
15. ANS: D              REF: Knowledge and Understanding        OBJ: 3.6 Mathematical Indices
LOC: ST2.01, ST5.03                      TOP: Tools for Analyzing Data
16. ANS: B              REF: Knowledge and Understanding        OBJ: 4.1 Experimental Probability
LOC: CP2.02, CP3.02                      TOP: Dealing with Uncertainty - An Introduction to
Probability
17. ANS: C              REF: Knowledge and Understanding        OBJ: 4.2 Theoretical Probability
LOC: CP1.08, CP2.01, CP2.03, CP2.06      TOP: Dealing with Uncertainty - An Introduction to
Probability
18. ANS: B              REF: Knowledge and Understanding        OBJ: 4.4 Conditional Probability
LOC: CP1.01, CP1.08, CP2.01, CP2.06      TOP: Dealing with Uncertainty - An Introduction to
Probability
19. ANS: A              REF: Knowledge and Understanding        OBJ: 4.5 Probability Using Diagrams
LOC: CP1.02, CP1.08, CP2.01, CP2.06      TOP: Dealing with Uncertainty - An Introduction to
Probability
20. ANS: B               REF: Knowledge and Understanding           OBJ: 4.5 Probability Using Diagrams
LOC: CP1.02, CP1.08, CP2.01, CP2.06        TOP: Dealing with Uncertainty - An Introduction to
Probability
21. ANS: C               REF: Knowledge and Understanding           OBJ: 4.6 Permutations and Probability
LOC: CP1.04, CP1.05, CP1.08                TOP: Dealing with Uncertainty - An Introduction to
Probability
22. ANS: D               REF: Knowledge and Understanding           OBJ: 4.7 Combinations and Probability
LOC: CP1.04, CP1.06, CP1.08, CP2.01        TOP: Dealing with Uncertainty - An Introduction to
Probability
23. ANS: B               REF: Knowledge and Understanding           OBJ: 4.7 Combinations and Probability
LOC: CP1.04, CP1.06, CP1.08, CP2.01        TOP: Dealing with Uncertainty - An Introduction to
Probability
24. ANS: B               REF: Knowledge and Understanding
OBJ: 5.1 Probability Distributions and Expected Value           LOC: CP2.04
TOP: Probability Distributions and Predictions
25. ANS: A               REF: Knowledge and Understanding
OBJ: 5.1 Probability Distributions and Expected Value           LOC: CP2.01
TOP: Probability Distributions and Predictions
26. ANS: D               REF: Knowledge and Understanding
OBJ: 5.1 Probability Distributions and Expected Value           LOC: CP2.01
TOP: Probability Distributions and Predictions
27. ANS: A               REF: Knowledge and Understanding
OBJ: 5.2 Pascal's Triangle and the Binomial Theorem             LOC: CP1.07
TOP: Probability Distributions and Predictions
28. ANS: C               REF: Application OBJ: 5.3 Binomial Distributions
LOC: CP2.05, CP2.06                        TOP: Probability Distributions and Predictions
29. ANS: B               REF: Knowledge and Understanding           OBJ: 5.3 Binomial Distributions
LOC: CP2.06          TOP: Probability Distributions and Predictions
30. ANS: D               REF: Knowledge and Understanding
OBJ: 5.4 Normal Approximation of the Binomial Distribution LOC: STV.03
TOP: Probability Distributions and Predictions

31. ANS:
The sampling method being used is systematic random sampling.

REF: Knowledge and Understanding               OBJ: 2.3 Collecting Samples
LOC: DMV.01, STV.01, ST1.01                    TOP: In Search of Good Data
32. ANS:
The interval with the greatest frequency is located at the centre of the histogram.

REF: Knowledge and Understanding           OBJ: 3.1 Graphical Displays of Information
LOC: ST3.01           TOP: Tools for Analyzing Data
33. ANS:
The median is the most appropriate measure of central tendency.

REF:    Knowledge and Understanding           OBJ: 3.2 Measures of Central Tendency
LOC: ST2.01            TOP: Tools for Analyzing Data
34. ANS:
The modal interval is 170–179.

REF: Knowledge and Understanding         OBJ: 3.2 Measures of Central Tendency
LOC: ST2.01           TOP: Tools for Analyzing Data
35. ANS:
This median will be \$150 000.

REF: Application OBJ: 3.2 Measures of Central Tendency                LOC: ST2.01
TOP: Tools for Analyzing Data
36. ANS:
The value of Q2 would be 15 and the value of Q3 would be 66.

REF: Application OBJ: 3.3 Measures of Spread                      LOC: ST2.01
TOP: Tools for Analyzing Data
37. ANS:
The possible numbers that represent a non-defective CD are 4 to 100.

REF: Knowledge and Understanding               OBJ: 4.1 Experimental Probability
LOC: CP2.02, CP3.02                            TOP: Dealing with Uncertainty - An Introduction to
Probability
38. ANS:
The probability of spinning a number other than an even number is       .

REF: Knowledge and Understanding               OBJ: 4.2 Theoretical Probability
LOC: CP1.08, CP2.01, CP2.03, CP2.06            TOP: Dealing with Uncertainty - An Introduction to
Probability
39. ANS:
The value of          is 1.

REF: Knowledge and Understanding               OBJ: 4.2 Theoretical Probability
LOC: CP1.08, CP2.01, CP2.03, CP2.06            TOP: Dealing with Uncertainty - An Introduction to
Probability
40. ANS:

The probability of rolling snake eyes is   .

REF: Knowledge and Understanding               OBJ: 4.5 Probability Using Diagrams
LOC: OD2.02, CP1.02, CP1.08, CP2.01            TOP: Dealing with Uncertainty - An Introduction to
Probability
41. ANS:

The probability that the spinner lands on A or B at least once is .

REF: Knowledge and Understanding               OBJ: 4.5 Probability Using Diagrams
LOC: OD2.02, CP1.02, CP1.08, CP2.01            TOP: Dealing with Uncertainty - An Introduction to
Probability
42. ANS:

The probability that the first and third children are boys is .

REF: Knowledge and Understanding              OBJ: 4.5 Probability Using Diagrams
LOC: OD2.02, CP1.02, CP1.08, CP2.01           TOP: Dealing with Uncertainty - An Introduction to
Probability
43. ANS:
n = 42

REF: Knowledge and Understanding         OBJ: 4.6 Permutations and Probability
LOC: CP1.04           TOP: Dealing with Uncertainty - An Introduction to Probability
44. ANS:
The odds of event A occurring is 3:4.

REF: Knowledge and Understanding              OBJ: 4.7 Combinations and Probability
LOC: CP1.08, CP2.01, CP2.06                   TOP: Dealing with Uncertainty - An Introduction to
Probability
45. ANS:

Sum            Probability
2               0.0625
3               0.125
4               0.1875
5               0.25
6               0.1875
7               0.125
8               0.0625

REF: Communication                   OBJ: 5.1 Probability Distributions and Expected Value
LOC: CP1.08      TOP: Probability Distributions and Predictions
46. ANS:

REF: Knowledge and Understanding      OBJ: 5.2 Pascal's Triangle and the Binomial Theorem
LOC: CP1.07       TOP: Probability Distributions and Predictions
47. ANS:

REF: Knowledge and Understanding      OBJ: 5.2 Pascal's Triangle and the Binomial Theorem
LOC: CP1.07       TOP: Probability Distributions and Predictions
48. ANS:
Three
REF: Knowledge and Understanding      OBJ: 5.2 Pascal's Triangle and the Binomial Theorem
LOC: CP1.07       TOP: Probability Distributions and Predictions
49. ANS:
0.169

REF: Application OBJ: 5.3 Binomial Distributions                      LOC: CP2.05
TOP: Probability Distributions and Predictions
50. ANS:
For 100 trials,  =                = 4.95. For 400 trials,  =                        = 9.90. When the number
of trials is increased by a factor k, the standard deviation of the normal approximation increases by   .

REF: Knowledge and Understanding      OBJ: 5.4 Normal Approximation of the Binomial Distribution
LOC: STV.03       TOP: Probability Distributions and Predictions

PROBLEM

51. ANS:
The 60 000 households should be numbered from 1 to 60 000. Then a random number generator or table
should be used to select 5-digit random integers. The starting position in the random number table (or seed for
the generator) should be randomly chosen. Then, as many random numbers should be taken as necessary from
the generator/table until 5 between 1 and 60 000 inclusive have been obtained (discarding numbers greater
than 60 000). The households labelled with these numbers form the sample.

REF: Knowledge and Understanding               OBJ: 2.3 Collecting Samples
LOC: DMV.01, STV.01, DM1.01                    TOP: In Search of Good Data
52. ANS:
In both cluster sampling and stratified sampling, the population is divided into groups—clusters or strata. In
cluster sampling, a simple random sample of the clusters is taken. Then every member of the population in the
chosen clusters forms the sample. In stratified sampling, every stratum is used. Then from each stratum, a
simple random sample of members of that stratum is chosen to participate.

REF: Thinking/Inquiry/PS                        OBJ: Chapter 2 Prob
LOC: STV.01, ST1.01                             TOP: In Search of Good Data
53. ANS:
The population is all adults in the city. The sample is the 1000 people who are surveyed. The variable to be
measured is the amount of fat consumed per day by each person in the sample. This will likely not be
measured directly, but by calculating fat content from a list of all foods and their quantities consumed by the
participants. The nutritionist should use multi-stage sampling. She needs to first take a sample of 1000
households. Then from each, she should take a sample of one adult. This is necessary because she has no list
of individuals. It may be more convenient to use cluster sampling for the choice of households where the
clusters are blocks. It would be quicker and cheaper to interview someone from every household on a block.
A simple random sample might mean she would have to interview people from households scattered across
the city.

REF: Knowledge and Understanding               OBJ: Chapter 2 Prob
LOC: STV.01, ST1.01                            TOP: In Search of Good Data
54. ANS:
In a double-blind experiment, both the researchers and the participants do not know which treatment is being
received. It may be possible to conceal the diet assigned to patients from the doctor conducting the
experiment. However, someone else must counsel the patient about what is to be eaten. Therefore, the patient
knows what diet they are to follow and so it is not blind to them.

REF: Communication                             OBJ: Chapter 2 Prob
LOC: DMV.01, STV.01, DM1.02                    TOP: In Search of Good Data
55. ANS:
The treatment group is the group taking aspirin. The control group is the group taking the pill with no active
ingredients. The placebo is the pill with no active ingredients. The experiment is double-blind because the
participants and the attending doctors do not know which pill is being taken by which participants.

REF: Knowledge and Understanding                OBJ: Chapter 2 Prob
LOC: DMV.01, STV.01, DM1.02                     TOP: In Search of Good Data
56. ANS:
Let x represent the fifth test mark and             .

The mark on the fifth test was 80.

REF: Application OBJ: 3.2 Measures of Central Tendency LOC: ST2.02
TOP: Tools for Analyzing Data
57. ANS:
Not necessarily, since he will use interval midpoints of 5.5, 15.5, et cetera as approximations instead of the
actual marks that were used by the teacher.

REF: Communication                            OBJ: 3.2 Measures of Central Tendency
LOC: ST2.01             TOP: Tools for Analyzing Data
58. ANS:
This statement is false in general. Counterexamples will vary but one example is:

If      1, 0, 1, the median = 0.
Then        1, 0, 1 and the median = 1.

REF: Thinking/Inquiry/PS                       OBJ: 3.2 Measures of Central Tendency
LOC: ST2.01             TOP: Tools for Analyzing Data
59. ANS:
Since the variance is the square of the standard deviation, it will be smaller if the standard deviation is
between 0 and 1. For example if      = 0.5, then       = 0.25.

REF: Knowledge and Understanding     OBJ: 3.3 Measures of Spread
LOC: ST2.01       TOP: Tools for Analyzing Data
60. ANS:
Let A be the event of being given a first interview and B be the event of being given a second interview. The
probability of being given a second interview is:
P(A B)

REF: Application OBJ: 4.4 Conditional Probability                    LOC: CP1.01, CP1.08, CP2.01, CP2.06
TOP: Dealing with Uncertainty - An Introduction to Probability
61. ANS:
A group of 24 people are asked whether they plan to retire before the age of 50 and if they are going to move
to a different house when they retire. The results were as follows. Determine the probability that a person
moves to a different house given that they are retiring before the age of 50.
Retiring Before Not Retiring Before
Residence
50 Years of Age          50 Years of Age
Moving to a different house               12                       1
Staying in the same house                  8                       4

REF: Thinking/Inquiry/PS                        OBJ: 4.4 Conditional Probability
LOC: CP1.01, CP1.08, CP2.01, CP2.06             TOP: Dealing with Uncertainty - An Introduction to
Probability
62. ANS:

But   must be positive, so      .

REF: Knowledge and Understanding                OBJ: 4.7 Combinations and Probability
LOC: CP1.03, CP1.04, CP1.08                     TOP: Dealing with Uncertainty - An Introduction to
Probability
63. ANS:
If the team wins a game, it gains confidence and the probability of the team winning its next game increases.
If the team loses a game, its confidence goes down and the probability of the team winning its next game
decreases. The probability of a team winning its next two games is the product of the probability that it will
win its next game multiplied by the probability of it winning its second game given that it has won its first.
This second probability will be more than 0.5 because it has gained confidence. Therefore, the probability of
the team winning its first game must be more than (0.5)(0.5) = 0.25.

REF: Communication                             OBJ: Chapter 4 Prob
LOC: CP2.01, CP2.06                            TOP: Dealing with Uncertainty - An Introduction to
Probability
64. ANS:

=                    +                    +                   +

+                    +

= 32x5 + 80x2 + 80x–1 + 40x–4 + 10x–7 + x–10

REF: Knowledge and Understanding      OBJ: 5.2 Pascal's Triangle and the Binomial Theorem
LOC: CP1.07       TOP: Probability Distributions and Predictions
65. ANS:

REF: Application OBJ: 5.3 Binomial Distributions                    LOC: CP2.05
TOP: Probability Distributions and Predictions
66. ANS:
a) There are sixteen possible outcomes.
1+1=2            2+1=3           3+1=4                4+1=5
1+2=3            2+2=4           3+2=5                4+2=6
1+3=4            2+3=5           3+3=6                4+3=7
1+4=5            2+4=6           3+4=7                4+4=8
b)
X       2          3         4       5             6        7         8
P(X)

c) E(X) = 2        +3        +4        +5        +6       +7        +8        =5

REF: Knowledge and Understanding               OBJ: Chapter 5 Prob
LOC: CPV.01, CP2.03                            TOP: Probability Distributions and Predictions
67. ANS:
A discrete variable takes on natural number values. The purpose of a binomial experiment is to determine the
number of successes in n trials. This must be a natural number. If we draw the graph of the probability
distribution and assign each bar a width of 1 and a height equal to the probability of that value of x, we will
have a total area for our graph of 1. The graph of the normal distribution has an area of 1 beneath a curve that
is defined by a continuous function. We need to identify the values where the edges of the bars meet the
curve. The centre of each bar is at the X value for that bar. The edges of each bar will be 0.5 to the right and
left of the centre. These edge values are converted to z-scores that allow us to go to the table of areas under
the normal curve.

REF: Communication                   OBJ: Chapter 5 Prob
LOC: ST2.03      TOP: Probability Distributions and Predictions

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