Deck 20: Probability and Combinatorics

Question 1

Business analytics combine "traditional" statistical methods with methods and
techniques from management science and information systems to form an interdisciplinary tool
that supports fact-based management decision making.

Answer 1

True

Question 2

Which of the following is not true about business analytics?

A) It enables you to use statistical methods to analyze and explore data to uncover unforeseen relationships.
B) It enables you to use management science methods to develop optimization models that impact an organization's strategy, planning, and operations.
C) It enables you to use complex mathematics to replace the need for organizational decision making and problem solving.
D) It enables you to use information systems methods to collect and process data sets of all sizes.

Answer 2

C

Question 3

Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But incidentals, such as textbook costs, are rarely considered. A researcher at Drummand
University wishes to estimate the textbook costs of first-year students at Drummand. To do so,
She monitored the textbook cost of 250 first-year students and found that their average textbook
Cost was $600 per semester. Identify the variable of interest to the researcher.

A) The textbook cost of first-year Drummand University students.
B) The year in school of Drummand University students.
C) The age of Drummand University students.
D) The cost of incidental expenses of Drummand University students.

Answer 3

A

Question 4

Managers need an understanding of statistics to be able to present and describe
information accurately, draw conclusions about large populations based on small samples,
improve processes, and make reliable forecasts.

Question 5

Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called

A) statistical inference.
B) DCOVA framework.
C) operational definition.
D) descriptive statistics.

Question 6

The Commissioner of Health in New York State wanted to study malpractice litigation in New
York. A sample of 31 thousand medical records was drawn from a population of 2.7 million
patients who were discharged during 2010. The collection, presentation, and characterization of
the data from patient medical records are examples of _______.

Question 7

The oranges grown in corporate farms in an agricultural state were damaged by some unknown
fungi a few years ago. Suppose the manager of a large farm wanted to study the impact of the
fungi on the orange crops on a daily basis over a 6-week period. On each day a random sample
of orange trees was selected from within a random sample of acres. The daily average number of
damaged oranges per tree and the proportion of trees having damaged oranges were calculated. In
this study, the presentation and characterization of the two main measures calculated each day
(i.e., average number of damaged oranges per tree and proportion of trees having damaged
oranges) is called _______ .

Question 8

A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights
Greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The
Study involves collecting heights from 250 randomly selected adult American pine trees and
Analyzing the results. Identify the variable of interest in the study.

A) The age of an American pine tree in Yosemite National Forest.
B) The height of an American pine tree in Yosemite National Forest.
C) The number of American pine trees in Yosemite National Forest.
D) The species of trees in Yosemite National Forest.

Question 9

The process of using data collected from a small group to reach conclusions about a large group is called

A) statistical inference.
B) DCOVA framework.
C) operational definition.
D) descriptive statistics.

Question 10

The estimation of the population average family expenditure on food based on the sample average expenditure of 1,000 families is an example of

A) inferential statistics.
B) descriptive statistics.
C) DCOVA framework.
D) operational definition.

Question 11

Compiling the number of registered voters who turned out to vote for the primary
in Iowa is an example of descriptive statistics.

Question 12

Problems may arise when statistically unsophisticated users who do not understand
the assumptions behind the statistical procedures or their limitations are misled by results
obtained from computer software.

Question 13

A professor computed the sample average exam score of 20 students and used it to
estimate the average exam score of the 1,500 students taking the exam. This is an example of
inferential statistics.

Question 14

Using the number of registered voters who turned out to vote for the primary in
Iowa to predict the number of registered voters who will turn out to vote in Vermont's primary is
an example of descriptive statistics.

Question 15

The Commissioner of Health in New York State wanted to study malpractice litigation in New
York. A sample of 31 thousand medical records was drawn from a population of 2.7 million
patients who were discharged during 2010. Using the information obtained from the sample to
predict population characteristics with respect to malpractice litigation is an example of _______.

Question 16

The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of

A) inferential statistics.
B) descriptive statistics.
C) operational definition.
D) DCOVA framework.

Question 17

The Human Resources Director of a large corporation wishes to develop an employee benefits
package and decides to select 500 employees from a list of all (N = 40,000) workers in order to
study their preferences for the various components of a potential package. In this study, methods
involving the collection, presentation, and characterization of the data are called _______.

Question 18

Which of the following is not an element of descriptive statistical problems?

A) An inference made about the population based on the sample.
B) The population or sample of interest.
C) Tables, graphs, or numerical summary tools.
D) Identification of patterns in the data.

Question 19

The oranges grown in corporate farms in an agricultural state were damaged by some unknown
fungi a few years ago. Suppose the manager of a large farm wanted to study the impact of the
fungi on the orange crops on a daily basis over a 6-week period. On each day a random sample
of orange trees was selected from within a random sample of acres. The daily average number of
damaged oranges per tree and the proportion of trees having damaged oranges were calculated. In
this study, drawing conclusions on any one day about the true population characteristics based on
information obtained from the sample is called _______.

Question 20

The Human Resources Director of a large corporation wishes to develop an employee benefits
package and decides to select 500 employees from a list of all (N = 40,000) workers in order to
study their preferences for the various components of a potential package. In this study, methods
that result in decisions concerning population characteristics based only on the sample results are
called _______.

Question 21

SCENARIO 4-13
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger
and 80 preferred chicken. 55 of the children preferred hamburger.
Referring to Scenario 4-13, assume we know that a person prefers chicken. The probability that
this individual is an adult is __________.

Question 22

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new
Machine produces 3 times as many widgets as the older machine does. Given a randomly chosen
Widget was tested and found to be defective, what is the probability it was produced by the new
Machine?

A) 0.08
B) 0.15
C) 0.489
D) 0.511

Question 23

SCENARIO 4-14
Suppose that patrons of a restaurant were asked whether they preferred water or whether they
preferred soda. 70% said that they preferred water. 60% of the patrons were male. 80% of the males
preferred water.
Referring to Scenario 4-14, suppose a randomly selected patron prefers soda. Then the probability
the patron is a male is __________.

Question 24

The D in the DCOVA framework stands for "define".

Question 25

SCENARIO 4-14
Suppose that patrons of a restaurant were asked whether they preferred water or whether they
preferred soda. 70% said that they preferred water. 60% of the patrons were male. 80% of the males
preferred water.
Referring to Scenario 4-14, suppose a randomly selected patron is a female. Then the probability
the patron prefers water is __________.

Question 26

The V in the DCOVA framework stands for "analyze".

Question 27

The C in the DCOVA framework stands for "collect".

Question 28

The O in the DCOVA framework stands for "operationalize".

Question 29

SCENARIO 4-13
A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or
chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger
and 80 preferred chicken. 55 of the children preferred hamburger.
Referring to Scenario 4-13, assume we know that a person prefers hamburger. The probability
that this individual is a child is __________.

Question 30

"Big data" is a concrete concept with a precise operational definition.

Question 31

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes
Over $50,000 and 70% had 2 cars. The probability that annual household income is over $50,000
If the residents of a household own 2 cars is:

A) 0.42
B) 0.48
C) 0.50
D) 0.69

Question 32

The V in the DCOVA framework stands for "visualize".

Question 33

The A in the DCOVA framework stands for "apply".

Question 34

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes
Over $50,000 and 70% had 2 cars. The probability that annual household income is over $50,000
If the residents of a household do not own 2 cars is:

A) 0.12
B) 0.18
C) 0.40
D) 0.70

Question 35

The O in the DCOVA framework stands for "organize".

Question 36

The C in the DCOVA framework stands for "categorize".

Question 37

The V in the DCOVA framework stands for "verify".

Question 38

"Big data" are data being collected in huge volumes and at very fast rates, and
they typically arrive in a variety of forms, organized and unorganized.

Question 39

In the current data-driven environment of business, the decisions you make will be
increasingly based on gut or intuition supported by personal experience.

Question 40

The D in the DCOVA framework stands for "data".

Question 41

There are 10 finalists at a national dog show. How many different orders of finishing can there
be for all the 10 finalists?

Question 42

Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory. Each room is
considered unique so that it matters who is being assigned to which room. How many different
ways can those eleven freshmen be allocated?

Question 43

SCENARIO 4-15
At a Texas college, 60% of the students are from the southern part of the state, 30% are from the
northern part of the state, and the remaining 10% are from out-of-state. All students must take and
pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the
northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM.
Referring to Scenario 4-15, if a randomly selected student has passed the ELM, the probability
the student is from out-of-state is ________.

Question 44

SCENARIO 4-15
At a Texas college, 60% of the students are from the southern part of the state, 30% are from the
northern part of the state, and the remaining 10% are from out-of-state. All students must take and
pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the
northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM.
Referring to Scenario 4-15, if a randomly selected student is not from out-of-state, the probability
the student has passed the ELM is ________.

Question 45

SCENARIO 4-16
According to the record of the registrar's office at a state university, 35% of the students are
freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen,
sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively,
80%, 60%, 30% and 20%.
Referring to Scenario 4-16, if a randomly selected student does not live in the dormitory, what is
the probability that the student is a junior or a senior?

Question 46

SCENARIO 4-17
Jake woke up late in the morning on the day that he has to go to school to take an important test. He
can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable
motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice.
Referring to Scenario 4-17, if Jake, in fact, gets to the test on time, what is the probability that he
took the bus?

Question 47

SCENARIO 4-16
According to the record of the registrar's office at a state university, 35% of the students are
freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen,
sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively,
80%, 60%, 30% and 20%.
Referring to Scenario 4-16, if a randomly selected student lives in the dormitory, what is the
probability that the student is not a freshman?

Question 48

A new model car from Ford Motor Company offers a keyless entry system that utilizes a four-
letter code. How many different possible combinations are there for the code?

Question 49

SCENARIO 4-10
Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were
black and 10% are other races. Given that a worker was white, the probability that the worker had
claimed bias was 30%. Given that a worker was black, the probability that the worker had claimed
bias was 40%. Given that a worker was other race, the probability that the worker had claimed bias
was 0%.
Referring to Scenario 4-10, if a randomly selected worker had not claimed bias, what is the
probability that the worker is white?

Question 50

At the International Pancakes Hut, there are 4 different ways to have an egg cooked, 7 different
choices of pancakes, 5 different types of syrups and 8 different beverages. How many different
ways are there to order an egg, a pancake with a choice of syrup and a beverage?

Question 51

SCENARIO 4-15
At a Texas college, 60% of the students are from the southern part of the state, 30% are from the
northern part of the state, and the remaining 10% are from out-of-state. All students must take and
pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the
northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM.
Referring to Scenario 4-15, if a randomly selected student is not from southern Texas, the
probability the student has not passed the ELM is ________.

Question 52

There are only 4 empty rooms available in a student dormitory for eleven new freshmen. All the
rooms are considered as homogenous so that it does not matter who is being assigned to which
room. How many different ways can those 4 empty rooms be filled one student per room?

Question 53

SCENARIO 4-17
Jake woke up late in the morning on the day that he has to go to school to take an important test. He
can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable
motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice.
Referring to Scenario 4-17, if Jake, in fact, gets to the test on time, what is the probability that he
rode his bike?

Question 54

SCENARIO 4-15
At a Texas college, 60% of the students are from the southern part of the state, 30% are from the
northern part of the state, and the remaining 10% are from out-of-state. All students must take and
pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the
northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM.
Referring to Scenario 4-15, if a randomly selected student has not passed the ELM, the
probability the student is from southern Texas is ________.

Question 55

There are only 4 empty rooms available in a student dormitory for eleven new freshmen. Each
room is considered unique so that it matters who is being assigned to which room. How many
different ways can those 4 empty rooms be filled one student per room?

Question 56

SCENARIO 4-16
According to the record of the registrar's office at a state university, 35% of the students are
freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen,
sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively,
80%, 60%, 30% and 20%.
Referring to Scenario 4-16, if a randomly selected student lives in the dormitory, what is the
probability that the student is a freshman?

Question 57

SCENARIO 4-10
Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were
black and 10% are other races. Given that a worker was white, the probability that the worker had
claimed bias was 30%. Given that a worker was black, the probability that the worker had claimed
bias was 40%. Given that a worker was other race, the probability that the worker had claimed bias
was 0%.
Referring to Scenario 4-10, if a randomly selected worker had claimed bias, what is the
probability that the worker is white?

Question 58

SCENARIO 4-15
At a Texas college, 60% of the students are from the southern part of the state, 30% are from the
northern part of the state, and the remaining 10% are from out-of-state. All students must take and
pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the
northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM.
Referring to Scenario 4-15, if a randomly selected student has not passed the ELM, the
probability the student is not from northern Texas is ________.

Question 59

SCENARIO 4-17
Jake woke up late in the morning on the day that he has to go to school to take an important test. He
can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable
motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice.
Referring to Scenario 4-17, if Jake is late to the test, what is the probability that he took the bus?

Question 60

SCENARIO 4-17
Jake woke up late in the morning on the day that he has to go to school to take an important test. He
can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable
motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice.
Referring to Scenario 4-17, if Jake is late to the test, what is the probability that he rode his bike?

Question 61

A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class.
How many possible ways can the team be formed which will include both of the twin brothers?

Question 62

The expected return of a two-asset portfolio is equal to the product of the weight
assigned to the first asset and the expected return of the first asset plus the product of the weight
assigned to the second asset and the expected return of the second asset.

Question 63

Twelve students in a Business Statistics class are to be formed into three teams of four. How
many different ways can this be done?

Question 64

A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class.
How many possible ways can the team be formed which will not include any of the twin
brothers?

Question 65

SCENARIO 5-11
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition. The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-11, what is the total variance of value gain if you invest in both houses?

Question 66

SCENARIO 5-11
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition. The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-11, what is the covariance of the two houses?

Question 67

The variance of the sum of two investments will be equal to the sum of the
variances of the two investments when the covariance between the investments is zero.

Question 68

There are 47 contestants at a national dog show. How many different ways can contestants fill
the first place, second place, and third place positions?

Question 69

A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class.
How many possible ways can the team be formed which will include only one of the twin
brothers?

Question 70

The expected return of the sum of two investments will be equal to the sum of the
expected returns of the two investments plus twice the covariance between the investments.

Question 71

The variance of the sum of two investments will be equal to the sum of the
variances of the two investments plus twice the covariance between the investments.

Question 72

Seven passengers are on a waiting list for an overbooked flight. As a result of cancellations, 3
seats become available. How many different ways can those 3 available seats be filled regardless
of the order?

Question 73

A high school debate team of 4 is to be chosen from a class of 35. How many possible ways can
the team be formed?

Question 74

The portfolio expected return of two investments

A) will be higher when the covariance is zero.
B) will be higher when the covariance is negative.
C) will be higher when the covariance is positive.
D) does not depend on the covariance.

Question 75

An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women
and 7 men. How many different ways can this team of 5 be formed?

Question 76

Four freshmen are to be assigned to eleven empty rooms in a student dormitory. All the rooms
are considered as homogenous so that it does not matter who is being assigned to which room.
How many different ways can those 4 freshmen be assigned?

Question 77

If the covariance between two investments is zero, the variance of the sum of the
two investments will be equal to the sum of the variances of the investments.

Question 78

The covariance between two investments is equal to the sum of the variances of the
investments.

Question 79

SCENARIO 5-11
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition. The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Referring to Scenario 5-11, what is the expected value gain if you invest in both houses?

Question 80

The covariance

A) must be between -1 and +1.
B) must be positive.
C) can be positive or negative.
D) must be less than +1.