QM Practice Problems 1
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Feb 20, 2024
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Quantitative Methods
Lecture 1 Practice Problems
1.
Exercise 2.9: Every person’s blood type is A, B, AB, or O. In addition, each individual either
has the Rhesus (Rh) factor (+) or does not (−). A medical technician records a person’s blood
type and Rh factor. List the sample space for this experiment.
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Quantitative Methods
2.
Exercise 2.13:
Americans can be quite suspicious, especially when it comes to government conspiracies. On the question of whether the U.S. Air Force has withheld proof of the existence of intelligent life on other planets, the proportions of Americans with varying opinions are given in the table.
Opinion
Proportion
Very likely
0.24
Somewhat likely
0.24
Unlikely
0.40
Other 0.12
Suppose that one American is selected and his or her opinion is recorded.
a.
What are the simple events for this experiment?
b.
Are the simple events that you gave in part (a) all equally likely? If not, what are the probabilities that should be assigned to each?
c.
What is the probability that the person selected finds it at least somewhat likely that the Air Force is withholding information about intelligent life on other planets?
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Quantitative Methods
3.
Exercise 2.33:
The Bureau of the Census reports that the median family income for all families in the United States during the year 2003 was $43,318. That is, half of all American families had incomes exceeding this amount, and half had incomes equal to or below this amount. Suppose that four families are surveyed and that each one reveals whether its income exceeded $43,318 in 2003.
a.
List the points in the sample space.
b.
Identify the simple events in each of the following events:
A
= At least two had incomes exceeding $43,318.
B
= Exactly two had incomes exceeding $43,318. C
= Exactly one had income less than or equal to $43,318.
c.
Make use of the given interpretation for the median to assign probabilities to the simple events and find P
(
A
), P
(
B
) and P
(
C
).
3
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Quantitative Methods
4.
Exercise 2.37:
A businesswoman in Philadelphia is preparing an itinerary for a visit to six major cities. The distance traveled, and hence the cost of the trip, will depend on the order in which she plans her route.
a.
How many different itineraries (and trip costs) are possible?
b.
If the businesswoman randomly selects one of the possible itineraries and Denver and San Francisco are two of the cities that she plans to visit, what is the probability that she will visit Denver before San Francisco?
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Quantitative Methods
5.
Exercise 2.49:
Students attending the University of Florida can select from 130 major areas of study. A student’s major is identified in the registrar’s records with a two-or three-letter code (for example, statistics majors are identified by STA, math majors by MS). Some students opt for a double major and complete the requirements for both of the major areas before graduation. The registrar was asked to consider assigning these double majors a distinct two- or three-letter code so that they could be identified through the student records’ system.
a.
What is the maximum number of possible double majors available to University of Florida students?
b.
If any two- or three-letter code is available to identify majors or double majors, how many major codes are available?
c.
How many major codes are required to identify students who have either a single major or a double major?
d.
Are there enough major codes available to identify all single and double majors at the University of Florida?
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Quantitative Methods
6.
Exercise 2.55:
A study is to be conducted in a hospital to determine the attitudes of nurses toward various administrative procedures. A sample of 10 nurses is to be selected from a total of the 90 nurses employed by the hospital.
a.
How many different samples of 10 nurses can be selected?
b.
Twenty of the 90 nurses are male. If 10 nurses are randomly selected from those employed by the hospital, what is the probability that the sample of ten will include exactly 4 male (and 6 female) nurses?
6
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Quantitative Methods
7.
Exercise 2.63:
The eight-member Human Relations Advisory Board of Gainesville, Florida, considered the complaint of a woman who claimed discrimination, based on sex, on the part of a local company. The board, composed of five women and three men, voted 5–3 in favor of the plaintiff, the five women voting in favor of the plaintiff, the three men against. The attorney representing the company appealed the board’s decision by claiming sex bias on the part of the board members. If there was no sex bias among the board members, it might be reasonable to conjecture that any group of five board members would be as likely to vote for the complainant as any other group of five. If this were the case, what is the probability that the vote would split along sex lines (five women for, three men against)?
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Quantitative Methods
8.
Exercise 2.67:
Refer to Example 2.13. Suppose that the number of distributors is M
= 10 and
that there are n
= 7 orders to be placed. What is the probability that:
a.
all of the orders go to different distributors?
b.
distributor I gets exactly two orders and distributor II gets exactly three orders?
c.
distributors I, II, and III get exactly two, three, and one order(s), respectively?
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