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# Basic Statistics for Business and Economics 6th Canadian Edition By Linda – Test Bank

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Basic Statistics for Business and Economics 6th Canadian Edition By Linda – Test Bank

Sample Questions

Chapter 02

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Multiple Choice Questions

1. (i) A frequency table is a grouping of qualitative data into mutually exclusive classes showing the number of observations in each class.
(ii) Simple bar charts may be constructed either horizontally or vertically.
(iii) A relative frequency table shows the fraction or percent of the number of observations in each class.
A.(i), (ii) and (iii) are all correct statements.
B. (i) and, (ii) are correct statements but not (iii).
C. (i) and, (iii) are correct statements but not (ii).
D. (ii) and, (iii) are correct statements but not (i).

Difficulty: Hard
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Learning Objective: 02-02 Display a frequency table using a bar or pie chart.
Topic: 02-02 Constructing A Frequency Table
Topic: 02-05 Bar Charts

1. (i) A frequency table is a grouping of qualitative data into mutually exclusive classes showing the number of observations in each class.
(ii) Simple bar charts may be constructed either horizontally or vertically.
(iii) A bar chart is a graphic representation of a frequency table.
A.(i), (ii) and (iii) are all correct statements.
B. (i) and, (ii) are correct statements but not (iii).
C. (i) and, (iii) are correct statements but not (ii).
D. (ii) and, (iii) are correct statements but not (i).

Difficulty: Hard
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Learning Objective: 02-02 Display a frequency table using a bar or pie chart.
Topic: 02-02 Constructing A Frequency Table
Topic: 02-05 Bar Charts

1. (i) Pie charts are useful for showing the percent that various components compose of the total.
(ii) Simple bar charts may be constructed either horizontally or vertically.
(iii) A bar chart is a graphic representation of a frequency table.
A.(i), (ii) and (iii) are all correct statements.
B. (i) and, (ii) are correct statements but not (iii).
C. (i) and, (iii) are correct statements but not (ii).
D. (ii) and, (iii) are correct statements but not (i).

Difficulty: Hard
Learning Objective: 02-02 Display a frequency table using a bar or pie chart.
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-05 Bar Charts
Topic: 02-06 Pie Charts

1. (i) Bar charts are useful for showing the percent that various components compose of the total.
(ii) Simple bar charts may be constructed either horizontally or vertically.
(iii) A bar chart is a graphic representation of a frequency table.
A.(i), (ii) and (iii) are all correct statements.
B. (i) and, (ii) are correct statements but not (iii).
C. (i) and, (iii) are correct statements but not (ii).
D. (ii) and, (iii) are correct statements but not (i).

Difficulty: Hard
Learning Objective: 02-02 Display a frequency table using a bar or pie chart.
Topic: 02-05 Bar Charts

1. (i) Bar charts are useful for showing the percent that various components compose of the total.
(ii) Simple bar charts may be constructed either horizontally or vertically.
(iii) A frequency polygon is ideal for showing the trend or sales of income over time.
A.(i), (ii) and (iii) are all correct statements.
B. (i) and, (ii) are correct statements but not (iii).
C. (i) and, (iii) are correct statements but not (ii).
D. (ii) and, (iii) are correct statements but not (i).

Difficulty: Hard
Learning Objective: 02-02 Display a frequency table using a bar or pie chart.
Learning Objective: 02-04 Display a frequency distribution using a histogram or frequency polygon.
Topic: 02-05 Bar Charts
Topic: 02-13 Histogram

1. Using the frequency table below, determine the relative frequencies for Apartment and Townhouse listings.
 Type Number Of Listings Apartment 58 House 26 Townhouse 14 98
1. 5000 and.5000
B. 5000 and.2653
C. 2653 and.1429
D. 1429 and.2495
E. 5918 and.1429

Difficulty: Medium
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-10 Relative Frequency Distribution

1. Quinn’s Café serves ice cream. She asks 100 of her regular customers to take a taste test and pick the flavour they like the best. The results are shown in the following table.
 Flavour Number Vanilla 40 Green tea 25 Lemon 20 Coffee 15 Total 100

Is the data quantitative or qualitative? What is the name of the table shown?
A. quantitative, simple table
B. quantitative, frequency table
C. qualitative, frequency table
D. qualitative, cumulative frequency distribution
E. quantitative, bar chart

Difficulty: Medium
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Topic: 02-02 Constructing A Frequency Table

1. When data is collected using a qualitative, nominal variable, i.e., male or female, what is true about a frequency distribution that summarizes the data?
A.Upper and lower class limits must be calculated.
B. Class midpoints can be computed.
C. Number of classes corresponds to number of the variable’s values.
D. The “2 to the k rule” can be applied.

Difficulty: Medium
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Topic: 02-02 Constructing A Frequency Table

1. A student was interested in the cigarette smoking habits of college students and collected data from an unbiased random sample of students. The data is summarized in the following table:
 Male:50 Female:75 Males who smoke: 20 Females who smoke: 25 Males who do not smoke: 30 Females who do not smoke: 50

Why is the table NOT a frequency table?
A. The number of males does not equal the sum of males that smoke and do not smoke.
B. The classes are not mutually exclusive.
C. There are too many classes.
D. Class limits cannot be computed

Difficulty: Medium
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Topic: 02-02 Constructing A Frequency Table

1. A group of 100 students were surveyed about their interest in a new International Studies program. The survey asked students about their interest in the program in terms of high, medium, or low. 30 students responded high interest; 50 students responded medium interest; 20 students responded low interest. What is the relative frequency of students with medium interest?
A.30%
B. 50%
C. 20%
D. Cannot be determined.

Difficulty: Easy
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Topic: 02-03 Relative Class Frequencies

1. Which of the following would be most helpful if you wished to construct a pie chart?
A.a frequency distribution
B. a relative frequency table
C. a cumulative frequency distribution
D. an ogive
E. a clustered bar chart

Difficulty: Medium
Learning Objective: 02-02 Display a frequency table using a bar or pie chart.
Topic: 02-06 Pie Charts

1. (i) A frequency distribution is grouping of data into classes showing the number of observations in each class.
(ii) The midpoint of a class, which is also called a class mark, is halfway between the lower and upper limits.
(iii) A class interval, which is the width of a class, can be determined by subtracting the lower limit of a class from the lower limit of the next higher class.
A.(i), (ii) and (iii) are all correct statements.
B. (i) and, (ii) are correct statements but not (iii).
C. (i) and, (iii) are correct statements but not (ii).
D. (ii) and, (iii) are correct statements but not (i).

Difficulty: Medium
Learning Objective: 02-04 Display a frequency distribution using a histogram or frequency polygon.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. (i) A frequency distribution is grouping of data into classes showing the number of observations in each class.
(ii) In constructing a frequency distribution, you should try to have open-ended classes such as “Under \$100” and “\$1,000 and over”.
(iii) A cumulative frequency distribution is used when we want to determine how many observations lie above or below certain values.
A.(i), (ii) and (iii) are all correct statements.
B. (i) and, (ii) are correct statements but not (iii).
C. (i) and, (iii) are correct statements but not (ii).
D. (ii) and, (iii) are correct statements but not (i).

Difficulty: Medium
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Learning Objective: 02-04 Display a frequency distribution using a histogram or frequency polygon.
Learning Objective: 02-05 Construct and interpret a cumulative frequency distribution.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data
Topic: 02-16 Cumulative Frequency Distribution

1. Monthly commissions of first-year insurance brokers are \$1,270, \$1,310, \$1,680, \$1,380, \$1,410, \$1,570, \$1,180 and \$1,420. These figures are referred to as:
A.histogram.
B. raw data.
C. frequency distribution.
D. frequency polygon.

Difficulty: Easy
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-02 Constructing A Frequency Table
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. The monthly incomes of a small sample of computer operators are \$1,950, \$1,775, \$2,060, \$1,840, \$1,795, \$1,890, \$1,925 and \$1,810. What are these ungrouped numbers called?
A.Histogram
B. Class limits
C. Class frequencies
D. Raw data

Difficulty: Easy
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-02 Constructing A Frequency Table
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. A group of 100 students were surveyed about their interest in a new International Studies program. The survey asked students about their interest in the program in terms of high, medium, or low. 30 students responded high interest; 50 students responded medium interest; 20 students responded low interest. What is the relative frequency of students with high interest?
A.30%
B. 50%
C. 20%
D. Cannot be determined.

Difficulty: Easy
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Topic: 02-03 Relative Class Frequencies

1. When a class interval is expressed as: 100 to under 200
A.Observations with values of 100 are excluded from the class frequency.
B. Observations with values of 200 are included in the class frequency.
C. Observations with values of 200 are excluded from the class frequency.
D. The class interval is 99.

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. What is the following table called?
 Ages Number of Ages 20 to under 30 16 30 to under 40 25 40 to under 50 51 50 to under 60 80 60 to under 70 20 70 to under 80 8
1. Histogram
B. Frequency polygon
C. Cumulative frequency distribution
D. Frequency distribution

Difficulty: Easy
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-02 Constructing A Frequency Table
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. A group of 100 students were surveyed about their interest in a new International Studies program. The survey asked students about their interest in the program in terms of high, medium, or low. 30 students responded high interest; 50 students responded medium interest; 20 students responded low interest. What is the relative frequency of students with low interest?
A.30%
B. 50%
C. 20%
D. Cannot be determined.

Difficulty: Easy
Learning Objective: 02-01 Summarize qualitative variables with frequency and relative frequency tables.
Topic: 02-03 Relative Class Frequencies

1. The monthly salaries of a sample of 100 employees were rounded to the nearest ten dollars. They ranged from a low of \$1,040 to a high of \$1,720. If we want to condense the data into seven classes, what is the most convenient class interval?
A.\$50
B. \$100
C. \$150
D. \$200

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. For the following distribution of heights, what are the limits for the class with the greatest frequency?
 Heights 60” to under 65” 65” to under 70” 70” to under 75” Number 10 70 20
1. 64 and 70
B. 65 and 69
C. 65 and 70
D. 69.5 and 74.5

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. In a frequency distribution, what is the number of observations in a class called?
A.Class midpoint
B. Class interval
C. Class array
D. Class frequency

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. A sample distribution of hourly earnings in Paul’s Cookie Factory is:
 Hourly Earnings \$6 to under \$9 \$9 to under \$12 \$12 to under \$15 Numbers 16 42 10

The limits of the class with the smallest frequency are:
A. \$6.00 and \$9.00
B. \$12.00 and \$14.00
C. \$11.75 and \$14.25
D. \$12.00 and \$15.00

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. Why are unequal class intervals sometimes used in a frequency distribution?
A.To avoid a large number of empty classes
B. For the sake of variety in presenting the data
C. To make the class frequencies smaller
D. To avoid the need for midpoints

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. Consider the following relative frequency distribution:
 Class Interval Relative Frequency 0 to under 10 0.2 10 to under 20 0.3 20 to under 30 0.45 30 to under 40 0.05

If there are 2,000 numbers in the data set, how many of the values are less than 30?
A. 900
B. 90
C. 1900
D. 100

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-10 Relative Frequency Distribution

1. Refer to the following price of jeans are recorded to the nearest dollar:
The first two class midpoints are \$62.50 and \$65.50.
What is the class interval?
A.\$1.00
B. \$2.00
C. \$2.50
D. \$3.00

Difficulty: Medium
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. Refer to the following price of jeans are recorded to the nearest dollar:
The first two class midpoints are \$62.50 and \$65.50.
What are the class limits for the lowest class?
A.\$61 and up to \$64
B. \$62 and up to \$64
C. \$62 and \$65
D. \$62 and \$63

Difficulty: Hard
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. Refer to the following price of jeans are recorded to the nearest dollar:
The first two class midpoints are \$62.50 and \$65.50.
What are the class limits for the third class?
A.\$64 and \$67
B. \$67 and \$69
C. \$67 and \$70
D. \$66 and \$68

Difficulty: Hard
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. Refer to the following ages (rounded to the nearest whole year) of employees at a large company that were grouped into a distribution with class limits:
20 up to 30
30 up to 40
40 up to 50
50 up to 60
60 up to 70

What is the class interval and the midpoint of the first class?
A.20 and 25
B. 20 and 24.5
C. 10 and 25
D. 10 and 24.5

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. What is the class midpoint for the \$45 up to \$55 class?
 Cost of Textbooks Number \$25 up to \$35 2 35 up to 45 5 45 up to 55 7 55 up to 65 20 65 up to 75 16
1. 49
B. 49.5
C. 50
D. 50.5

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. What are the class limits for the \$55 up to \$65 class?
 Cost of Textbooks Number \$25 up to \$35 2 35 up to 45 5 45 up to 55 7 55 up to 65 20 65 up to 75 16
1. 55 and 64
B. 54 and 64
C. 55 and up to 65
D. 55 and 64.5

Difficulty: Easy
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. The following class intervals for a frequency distribution were developed to provide information regarding the starting salaries for students graduating from a particular school:
 Salary (\$1,000s) Number of Graduates 18-under 21 – 21-under 25 – 24-under 27 – 29-under 30 –

Before data was collected, someone questioned the validity of this arrangement. Which of the following represents a problem with this set of intervals?
A. there are too many intervals
B. the class widths are too small
C. some numbers between 18,000 and 30,000 would fall into two different intervals
D. the first and the second interval overlap

Difficulty: Medium
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. The following class intervals for a frequency distribution were developed to provide information regarding the starting salaries for students graduating from a particular school:
 Salary (\$1,000s) Number of Graduates 18-under 21 – 21-under 25 – 24-under 27 – 29-under 30 –

Before data was collected, someone questioned the validity of this arrangement. Which of the following represents a problem with this set of intervals?
A. there are too many intervals
B. the class widths are too small
C. some numbers between 18,000 and 30,000 would not fall into any of these intervals
D. the first and the second intervals overlap
E. the second and third intervals overlap

Difficulty: Medium
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. The head of the statistics department wants to determine the number of mistake made by students in their first online assignment. She gathers information from her classes of the past year.
 Errors Per Assignment Number of Students 0 to under 2 40 2 to under 4 50 4 to under 6 30 6 to under 8 10 8 to under 10 20

The approximate range (distance from the minimum value in the raw data up to the maximum value) of the data is _________.
A. 150
B. 40
C. 10
D. 2

Difficulty: Medium
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-08 Constructing Frequency Distributions: Quantitative Data

1. Refer to the following distribution of commissions:
 Monthly commissions Class Frequencies \$600 to under \$800 3 800 to under 1,000 7 1,000 to under 1,200 11 1,200 to under 1,400 22 1,400 to under 1,600 40 1,600 to under 1,800 24 1,800 to under 2,000 9 2,000 to under 2,200 4

What is the relative frequency for those salespersons that earn between \$1,600 and \$1,799?
A. 2%
B. 2.4%
C. 20%
D. 24%

Difficulty: Medium
Learning Objective: 02-03 Summarize quantitative variables with frequency and relative frequency distributions.
Topic: 02-10 Relative Frequency Distribution

Chapter 04

A Survey of Probability Concepts

Multiple Choice Questions

1. i. A probability is usually expressed as a decimal, such as 0.70 or 0.27, but it may be given as a fraction, such as 7/10 or 27/100.
2. The closer a probability is to 0, the more likely that an event will happen.

iii. The closer the probability is to 1.00, the more likely an event will not happen.

1. (i), (ii) and (iii) are all correct statements
2. (i) is a correct statement but not (ii) or (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Medium

Learning Objective: 04-01 Define the terms probability; experiment; event; and outcome.

Topic: 04-01 What is a Probability?

1. i. A probability is usually expressed as a decimal, such as 0.70 or 0.27, but it may be given as a fraction, such as 7/10 or 27/100.
2. The probability of 1 represents something that is certain to happen.

iii. The probability of 0 represents something that cannot happen.

1. (i), (ii) and (iii) are all correct statements
2. (i) is a correct statement but not (ii) or (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Medium

Learning Objective: 04-01 Define the terms probability; experiment; event; and outcome.

Topic: 04-01 What is a Probability?

1. i. A probability is usually expressed as a decimal, such as 0.70 or 0.27, but it may be given as a fraction, such as 7/10 or 27/100.
2. The closer a probability is to 0, the more likely that an event will not happen.

iii. The closer the probability is to 1.00, the more likely an event will happen.

1. (i), (ii) and (iii) are all correct statements
2. (i) is a correct statement but not (ii) or (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Medium

Learning Objective: 04-01 Define the terms probability; experiment; event; and outcome.

Topic: 04-01 What is a Probability?

1. i. The probability of an event, based on a classical approach, is defined as the number of favourable outcomes divided by the total number of possible outcomes.
2. If among several events only one can occur at a time, we refer to these events as being mutually exclusive events.

iii. The probability of rolling a 3 or 2 on a single die is an example of conditional probability.

1. (i), (ii) and (iii) are all correct statements
2. (i) and, (ii) are correct statements but not (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Hard

Learning Objective: 04-02 Assign probabilities using a classical; empirical or subjective approach.

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-02 Approaches to Assigning Probabilities

Topic: 04-03 Classical Probability

Topic: 04-07 Principles of Counting

Topic: 04-20 General Rule of Multiplication

1. i. A subjective probability can be assigned to an event by an individual based on the individual’s knowledge about the event.
2. The probability that you would assign to the likelihood that the Hamilton Tiger Cats will be in the Grey Cup this season must be between 0 and 10.

iii. A probability is a number from -1 to +1 inclusive that measures one’s belief that an event resulting from an experiment will occur.

1. (i), (ii) and (iii) are all correct statements
2. (i) and, (ii) are correct statements but not (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Hard

Learning Objective: 04-01 Define the terms probability; experiment; event; and outcome.

Learning Objective: 04-02 Assign probabilities using a classical; empirical or subjective approach.

Topic: 04-01 What is a Probability?

Topic: 04-05 Subjective Probability

1. i. The Cunard luxury liner, Queen Elizabeth 2, cannot be docked in Hong Kong and Bangkok at the same time. Events such as these that cannot occur simultaneously are said to be collectively exhaustive.
2. If there are ‘m’ ways of doing one thing and ‘n’ ways of doing another thing, the multiplication formula states that there are (m)(n) ways of doing both.

iii. A permutation is an arrangement of a set of objects in which there is an order from the first through the last.

1. (i), (ii) and (iii) are all correct statements
2. (i) and, (ii) are correct statements but not (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Hard

Learning Objective: 04-02 Assign probabilities using a classical; empirical or subjective approach.

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-03 Classical Probability

Topic: 04-08 The Multiplication Formula

Topic: 04-09 The Permutation Formula

1. An electronics firm manufactures three models of stereo receivers, two cassette decks, four speakers and three CD players. When the four types of components are sold together, they form a “system.” How many different systems can the electronic firm offer?
2. 36
3. 18
4. 72
5. 144

Difficulty: Medium

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-08 The Multiplication Formula

1. The numbers 0 through 9 are to be used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?
2. 5,040
3. 620
4. 10,200
5. 120

Difficulty: Medium

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-08 The Multiplication Formula

1. There are two letters C and D. If repetitions such as CC are permitted, how many permutations are possible?
2. 1
3. 0
4. 4
5. 8

Difficulty: Medium

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-09 The Permutation Formula

1. You have the assignment of designing colour codes for different parts. Three colours are to be used on each part, but a combination of three colours used for one part cannot be rearranged and used to identify a different part. This means that if green, yellow and violet were used to identify a camshaft, yellow, violet and green (or any other combination of these three colours) could not be used to identify a pinion gear. If there are 35 combinations, how many colours were available?
2. 5
3. 7
4. 9
5. 11

Difficulty: Hard

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-10 The Combination Formula

1. A builder has agreed not to erect all “lookalike” homes in a new subdivision. Five exterior designs are offered to potential homebuyers. The builder has standardized three interior plans that can be incorporated in any of the five exteriors. How many different ways are the exterior and interior plans offered to potential homebuyers?
2. 8
3. 10
4. 15
5. 30

Difficulty: Medium

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-08 The Multiplication Formula

1. Six basic colours are to be used in decorating a new condominium. They are to be applied to a unit in groups of four colours. One unit might have gold as the principal colour, blue as a complementary colour, red as the accent colour and touches of white. Another unit might have blue as the principal colour, white as the complimentary colour, gold as the accent colour and touches of red. If repetitions are permitted, how many different units can be decorated?
2. 7,825
3. 24
4. 125
5. 1,296

Difficulty: Hard

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-08 The Multiplication Formula

1. Six basic colours are to be used in decorating a new condominium. They are to be applied to a unit in groups of four colours. One unit might have gold as the principal colour, blue as a complementary colour, red as the accent colour and touches of white. Another unit might have blue as the principal colour, white as the complimentary colour, gold as the accent colour and touches of red. If repetitions are not permitted, how many different units can be decorated?
2. 360
3. 25
4. 125
5. 1,296

Difficulty: Hard

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-08 The Multiplication Formula

1. Consideration is being given to forming a Super Ten Basketball Conference. The top 10 university basketball teams in the country, based on past records, would be members of the Super Ten Conference. Each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. How many games would the conference commissioner have to schedule each year? (Remember, McMaster versus Alberta is the same as Alberta versus McMaster.)
2. 45
3. 50
4. 125
5. 14

Difficulty: Medium

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-10 The Combination Formula

1. A rug manufacturer has decided to use 7 compatible colours in her rugs. However, in weaving a rug, only 5 spindles can be used. In advertising, the rug manufacturer wants to indicate the number of different colour groupings for sale. How many colour groupings using the seven colours taken five at a time are there? (This assumes that 5 different colours will go into each rug, i.e., there are no repetitions of colour.)
2. 120
3. 2,520
4. 6,740
5. 36

Difficulty: Hard

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-10 The Combination Formula

1. i. An experiment is an activity that is either observed or measured.
2. If an experiment, such as a die-tossing experiment, has a set of events that includes every possible outcome, the set of events is called collectively exhaustive.

iii. The combination formula is: n!/(n – r)!

1. (i), (ii) and (iii) are all correct statements
2. (i) and, (ii) are correct statements but not (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Medium

Learning Objective: 04-02 Assign probabilities using a classical; empirical or subjective approach.

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-03 Classical Probability

Topic: 04-10 The Combination Formula

1. i. An illustration of an experiment is turning the ignition key of an automobile as it comes off the assembly line to determine whether or not the engine will start.
2. If there are ‘m’ ways of doing one thing and ‘n’ ways of doing another thing, the multiplication formula states that there are (m)*(n) ways of doing both.

iii. A permutation is an arrangement of a set of objects in which there is an order from the first through the last.

1. (i), (ii) and (iii) are all correct statements
2. (i) and, (ii) are correct statements but not (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Hard

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-08 The Multiplication Formula

Topic: 04-09 The Permutation Formula

1. A sales representative calls on four hospitals in York Region. It is immaterial what order he calls on them. How many ways can he organize his calls?
2. 4
3. 24
4. 120
5. 37

Difficulty: Medium

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-10 The Combination Formula

1. i. The Cunard luxury liner, Queen Elizabeth 2, cannot be docked in Hong Kong and Bangkok at the same time. Events such as these that cannot occur simultaneously are said to be mutually exclusive.
2. If there are ‘m’ ways of doing one thing and ‘n’ ways of doing another thing, the multiplication formula states that there are (m) • (n) ways of doing both.

iii. A permutation is an arrangement of a set of objects in which order does not matter.

1. (i), (ii) and (iii) are all correct statements
2. (i) and, (ii) are correct statements but not (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Hard

Learning Objective: 04-02 Assign probabilities using a classical; empirical or subjective approach.

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-03 Classical Probability

Topic: 04-07 Principles of Counting

Topic: 04-08 The Multiplication Formula

Topic: 04-09 The Permutation Formula

1. What does equal?
2. 640
3. 36
4. 10
5. 120

Difficulty: Medium

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-09 The Permutation Formula

1. The result of a particular experiment is called a(n)
2. observation.
3. conditional probability.
4. event.
5. outcome.

Difficulty: Easy

Learning Objective: 04-01 Define the terms probability; experiment; event; and outcome.

Topic: 04-02 Approaches to Assigning Probabilities

1. When are two events mutually exclusive?
2. They overlap on a Venn diagram
3. If one event occurs, then the other cannot
4. Probability of one affects the probability of the other
5. They both happen at the same time

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-14 Special Rule of Addition

1. The National Centre for Health Statistics reported that of every 883 deaths in recent years, 24 resulted from an automobile accident, 182 from cancer and 333 from heart disease. Using the relative frequency approach, what is the probability that a particular death is due to an automobile accident?
2. 24/883 or 0.027
3. 539/883 or 0.610
4. 24/333 or 0.072
5. 182/883 or 0.206

Difficulty: Medium

Learning Objective: 04-02 Assign probabilities using a classical; empirical or subjective approach.

Topic: 04-04 Empirical Probability

1. Which approach to probability is exemplified by the following formula?

Probability of Event Happening =      Number of times event occurred in past

Total number of observations

1. Classical approach
2. Empirical approach
3. Subjective approach

Difficulty: Medium

Learning Objective: 04-02 Assign probabilities using a classical; empirical or subjective approach.

Topic: 04-04 Empirial Probability

1. A study of 200 stamping firms revealed these incomes after taxes:

Income After Taxes    Number of Firms

Under \$1 million         102

\$1 million to under \$20 million           61

\$20 million and more  37

What is the probability that a particular firm selected has \$1 million or more in income after taxes?

1. 0.00
2. 0.25
3. 0.49
4. 0.51

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-14 Special Rule of Addition

1. According to which classification or type of probability are the events equally likely?
2. Classical
3. Empirical
4. Subjective
5. Mutually exclusive

Difficulty: Medium

Learning Objective: 04-01 Define the terms probability; experiment; event; and outcome.

Topic: 04-02 Approaches to Assigning Probabilities

1. The first card selected from a standard 52-card deck was a king. If it is returned to the deck, what is the probability that a king will be drawn on the second selection?
2. 1/4 or 0.25
3. 1/13 or 0.077
4. 12/13 or 0.923
5. 1/3 or 0.33

Difficulty: Medium

Learning Objective: 04-02 Assign probabilities using a classical; empirical or subjective approach.

Topic: 04-03 Classical Probability

1. A group of employees of Unique Services is to be surveyed with respect to a new pension plan. In-depth interviews are to be conducted with each employee selected in the sample. The employees are classified as follows.

Classification  Event   Number of Employees

Supervisors      A         120

Maintenance    B         50

Production      C         1,460

Management   D         302

Secretarial       E          68

What is the probability that the first person selected is classified as a maintenance employee?

1. 0.20
2. 0.50
3. 0.025
4. 1.00

Difficulty: Medium

Learning Objective: 04-02 Assign probabilities using a classical; empirical or subjective approach.

Topic: 04-04 Empirial Probability

1. A lamp manufacturer has developed five lamp bases and four lampshades that could be used together. How many different arrangements of base and shade can be offered?
2. 5
3. 10
4. 15
5. 20

Difficulty: Medium

Learning Objective: 04-03 Determine the number of outcomes using principles of counting.

Topic: 04-08 The Multiplication Formula

1. When two or more events can occur concurrently it is called
2. conditional probability.
3. empirical probability.
4. joint probability.
5. a tree diagram.

Difficulty: Easy

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-16 The General Rule of Addition

1. When an event’s probability depends on the likelihood of another event, the probability is
2. conditional probability.
3. empirical probability.
4. joint probability.
5. Mutually exclusive probability.

Difficulty: Easy

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-20 General Rule of Multiplication

1. A board of directors consists of eight men and four women. A four-member search committee is to be chosen at random to recommend a new company president. What is the probability that all four members of the search committee will be women?
2. 1/120 or 0.00083
3. 1/16 or 0.0625
4. 1/8 or 0.125
5. 1/495 or 0.002

Difficulty: Medium

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-19 Special Rule of Multiplication

1. When an experiment is conducted “without replacement”,
2. events are independent
3. events are equally likely
4. the experiment can be illustrated with a Venn Diagram
5. the probability of two or more events is computed as a joint probability

Difficulty: Medium

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-18 Rules of Multiplication

1. What does the complement rule state?
2. P(A) = P(A) -P(B)
3. P(A) = 1 -P (not A)
4. P(A) = P(A) • P(B)
5. P(A) = P(A)X + P(B)

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-15 Complement Rule

1. i. The complement rule states that the probability of an event not occurring is equal to one minus the probability of its occurrence.
2. If there are two independent events A and B, the probability that A and x B will occur is found by multiplying the two probabilities. Thus for two events A and B, the special rule of multiplication shown symbolically is: P(A and B) = P(A) P(B).

iii. The general rule of multiplication is used to find the joint probability that two events will occur. Symbolically, the joint probability P(A and B) is found by: P(A and B) = P(A)P(B/A).

1. (i), (ii) and (iii) are all correct statements
2. (i) and, (ii) are correct statements but not (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Hard

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-15 Complement Rule

Topic: 04-19 Special Rule of Multiplication

Topic: 04-20 General Rule of Multiplication

1. Routine physical examinations are conducted annually as part of a health service program for the employees. It was discovered that 8% of the employees needed corrective shoes, 15% needed major dental work and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?
2. 0.20
3. 0.25
4. 0.50
5. 1.00

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-16 The General Rule of Addition

1. There are 10 rolls of film in a box and 3 are defective. Two rolls are to be selected one after the other. What is the probability of selecting a defective roll followed by another defective roll?
2. 1/2 or 0.50
3. 1/4 or 0.25

Difficulty: Medium

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-19 Special Rule of Multiplication

1. Giorgio offers the person who purchases a 250 ml bottle of Allure two free gifts, either an umbrella, a 30 ml bottle of Midnight, a feminine shaving kit, a raincoat or a pair of rain boots. If you purchased Allure what is the probability you selected at random an umbrella and a shaving kit in that order?
2. 0.00
3. 1.00
4. 0.05
5. 0.20

Difficulty: Medium

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-18 Rules of Multiplication

1. The machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixed. Sue and Jim approached the machine first. They both said they wanted red gum balls. What is the likelihood they will get their wish?
2. 0.50
3. 0.062
4. 0.33
5. 0.75

Difficulty: Medium

Learning Objective: 04-06 Compute probabilities using a contingency table.

Topic: 04-18 Rules of Multiplication

1. A survey of top executives revealed that 35% of them regularly read Time magazine, 20% read Newsweek and 40% read Macleans & World Report. Ten percent read both Time and Macleans. What is the probability that a particular top executive reads either Time or Macleans regularly?
2. 0.85
3. 0.06
4. 1.00
5. 0.65

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-16 The General Rule of Addition

1. A study by Tourism Ontario revealed that 50% of the vacationers going to Toronto visit the CN Tower, 40% visit SkyDome and 35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?
2. 0.95
3. 0.35
4. 0.55
5. 0.05

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-16 The General Rule of Addition

1. i. A coin is tossed four times. The probability is ¼ or 0.25 that all four tosses will result in a head face up.
2. A coin is tossed four times. The probability is 1/8 or 0.125 that all four tosses will result in a head face up.

iii. If two events are mutually exclusive, then P(A or B) = P(A)P(B).

1. (i), (ii) and (iii) are all correct statements
2. (i) and, (ii) are correct statements but not (iii).
3. (i) and, (iii) are correct statements but not (ii).
4. (ii) and, (iii) are correct statements but not (i).
5. (i), (ii) and (iii) are all false statements.

Difficulty: Medium

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-18 Rules of Multiplication

Topic: 04-19 Special Rule of Multiplication

1. A tire manufacturer advertises, “the median life of our new all-seasonradial tire is 120,000 km. An immediate adjustment will be made on any tire that does not last 120,000 km.” You purchased four of these tires. What is the probability that all four tires will wear out before traveling 120,000 km?
2. 1/10 or 0.10
3. ¼ or 0.25
4. 1/64 or 0.0156
5. 1/16 or 0.0625

Difficulty: Medium

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-18 Rules of Multiplication

1. Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective?
2. 3/20 or 0.15
3. 3/17 or 0.176
4. 1/4 or 0.25
5. 3/190 or 0.01579

Difficulty: Medium

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-18 Rules of Multiplication

1. If two events are independent, then their joint probability is
2. computed with the special rule of addition
3. computed with the special rule of multiplication
4. computed with the general rule of multiplication
5. computed with Bayes theorem

Difficulty: Medium

Learning Objective: 04-05 Calculate probabilities using the rules of multiplication.

Topic: 04-19 Special Rule of Multiplication

1. When applying the special rule of addition for mutually exclusive events, the joint probability is:
2. 1
3. 5
4. 0
5. 0.25
6. unknown

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-14 Special Rule of Addition

1. A group of employees of Unique Services is to be surveyed with respect to a new pension plan. In-depth interviews are to be conducted with each employee selected in the sample. The employees are classified as follows.

Classification  Event   Number of Employees

Supervisors      A         120

Maintenance    B         50

Production      C         1,460

Management   D         302

Secretarial       E          68

What is the probability that the first person selected is either in maintenance or in secretarial?

1. 0.200
2. 0.015
3. 0.059
4. 0.001

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-14 Special Rule of Addition

1. A group of employees of Unique Services is to be surveyed with respect to a new pension plan. In-depth interviews are to be conducted with each employee selected in the sample. The employees are classified as follows.

Classification  Event   Number of Employees

Supervisors      A         120

Maintenance    B         50

Production      C         1,460

Management   D         302

Secretarial       E          68

What is the probability that the first person selected is in management and in supervision?

1. 0.00
2. 0.06
3. 0.15
4. 0.21

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-14 Special Rule of Addition

1. A group of employees of Unique Services is to be surveyed with respect to a new pension plan. In-depth interviews are to be conducted with each employee selected in the sample. The employees are classified as follows.

Classification  Event   Number of Employees

Supervisors      A         120

Maintenance    B         50

Production      C         1,460

Management   D         302

Secretarial       E          68

What is the probability that the first person selected is a supervisor and in production?

1. 0.00
2. 0.06
3. 0.15
4. 0.21

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-14 Special Rule of Addition

1. Each salesperson in a large department store chain is rated with respect to sales potential for advancement. These traits for the 500 salespeople were cross classified into the following table.

Sales Ability    Fair      Good   Excellent

Below average            16        12        22

Average           45        60        45

Above average            93        72        135

What is the probability that a salesperson selected at random has above average sales ability and is an excellent potential for advancement?

1. 0.20
2. 0.50
3. 0.27
4. 0.75

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-21 Contingency Tables

1. Each salesperson in a large department store chain is rated with respect to sales potential for advancement. These traits for the 500 salespeople were cross classified into the following table.

Sales Ability    Fair      Good   Excellent

Below average            16        12        22

Average           45        60        45

Above average            93        72        135

What is the probability that a salesperson selected at random will have average sales ability and good potential for advancement?

1. 0.09
2. 0.12
3. 0.30
4. 0.525

Difficulty: Medium

Learning Objective: 04-04 Calculate probabilities using the rules of addition.

Topic: 04-21 Contingency Tables

1. Each salesperson in a large department store chain is rated with respect to sales potential for advancement. These traits for the 500 salespeople were cross classified into the following table.

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