# Multiple Choice Questions on Decision Science

1. Random numbers generated by a mathematical process instead of a physical process are pseudorandom numbers.

True

False

2. In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution.

True

False

3. Two events that are independent cannot be mutually exclusive.

True

False

4. Experimental outcomes must occur as numerical values in order to define their probability distribution.

True

False

5. A joint probability can have a value greater than 1.

True

False

6. A random variable that can take on any value along a line segment is a continuous random variable.

True

False

7. Sample information with an efficiency rating of 100% is perfect information.

True

False

8. States of nature should be defined so that one and only one will actually occur.

True

False

9. Time series methods base forecasts only on past values of the variables.

True

False

10. Random variations are movements that are not predictable and follow no pattern.

True

False

11. The field of decision science

a-concentrates on the use of quantitative methods to assist in decision making.

b-approaches decision making rationally, with techniques based on the scientific method.

c-is another name for management science and for operations research.

d-each of the above is true.

12. Identification and definition of a problem

a-cannot be done until alternatives are proposed.

b- is the first step of decision making.

c-is the final step of problem solving.

d-requires consideration of multiple criteria.

13. The appropriate decision criterion is dependent on

a-the risk personality of the decision maker.

b-the philosophy of the decision maker.

c-all of the above.

d-none of the above.

14. Decision criteria

a-are the choices faced by the decision maker.

b-are the problems faced by the decision maker.

c-are the ways to evaluate the choices faced by the decision maker.

d-must be unique for a problem.

15. The term opportunity loss is most closely related to

a-maximin regret.

b-maximax regret.

c-minimax regret.

d-minimin regret.

16. Which of the following is not a valid representation of a probability?

a-35%

b- 0

c-1.04

d- 3/8

17. A ___________ probability distribution indicates the probability of r successes in n trials.

a- joint.

b- subjective.

c- marginal.

d- binomial.

18. Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

Job Male (M) Female (F)

Administrative (AD) 110 10

Salaried staff (SS) 30 50

Hourly staff (HS) 60 40

If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member.

a- .1667

b-.5

c- .6

d- .625

e- .7

19. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The complement of A is

a- all new customers.

b- all accounts fewer than 31 or more than 60 days past due.

c- all accounts from new customers and all accounts that are from 31 to 60 days past due.

d- all new customers whose accounts are between 31 and 60 days past due.

20. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The union of A and B is

a- all new customers.

b- all accounts fewer than 31 or more than 60 days past due.

c- all accounts from new customers and all accounts that are from 31 to 60 days past due.

d- all new customers whose accounts are between 31 and 60 days past due.

21. A numerical description of the outcome of an experiment is

a-a normal variable.

b-a discrete variable.

c-a random variable.

d-an experimental variable.

22. Which of the following are continuous random variables?

I. the weight of an elephant

II. the time to answer a questionnaire

III. the number of floors in a skyscraper

IV. the square feet of countertop in a kitchen

a- I and II only

b-I and III only

c- I, II and IV

d- I, II, III, and IV

23. A statement that matches the values of a random variable with the probabilities of those values is

a-the expected value.

b-the variation of the random variable.

c-an experiment.

d-a probability distribution.

24. In order to measure the dispersion of a random variable, look at its

a-standard deviation.

b-mean.

c-expected value.

d-average.

25. Experiments with repeated independent trials will be described by the binomial distribution if

a- the trials are continuous.

b- each trial result influences the next.

c- the time between trials is constant.

d- each trial has exactly two outcomes whose probabilities do not change.

26. The options from which a decision maker chooses a course of action are

a-called the decision alternatives.

b-under the control of the decision maker.

c-not the same as the states of nature.

d-each of the above is true.

27. States of nature

a-can describe uncontrollable natural events such as floods or freezing temperatures.

b-can be selected by the decision maker.

c-cannot be enumerated by the decision maker.

d-each of the above is true.

28. A payoff

a- is always measured in profit.

b- is always measured in cost.

c- exists for each pair of decision alternative and state of nature.

d- exists for each state of nature.

29. Making a good decision

a- requires probabilities for all states of nature.

b- requires a clear understanding of decision alternatives, states of nature, and payoffs.

c- implies that a desirable outcome will occur.

d- each of the above is true.

30. A decision tree

a- presents all decision alternatives first and follows them with all states of nature.

b- presents all states of nature first and follows them with all decision alternatives.

c-alternates the decision alternatives and states of nature.

d- arranges decision alternatives and states of nature in their natural chronological order.

31. Time series methods

a- discover a pattern in historical data and project it into the future.

b-include cause-effect relationships.

c- are useful when historical information is not available.

d- each of the above is true.

32. Gradual shifting of a time series over a long period of time is called

a- periodicity.

b- cycle.

c- regression.

d- trend.

33. Seasonal components

a- cannot be predicted.

b- are regular repeated patterns.

c- are long runs of observations above or below the trend line.

d- reflect a shift in the series over time.

34. Short-term, unanticipated, and nonrecurring factors in a time series provide the random variability known as

a-uncertainty.

b-the forecast error.

c-the residuals.

d- the irregular component.

35. The focus of smoothing methods is to smooth

a- the irregular component.

b- wide seasonal variations.

c- significant trend effects.

d- long range forecasts.

36. Forecast errors

a- are the difference in successive values of a time series.

b-are the differences between actual and forecast values .

c-should all be nonnegative .

d- should be summed to judge the goodness of a forecasting model.

37. Which of the methods for decision making without probabilities best protects the decision maker from undesirable results?

a- the optimistic approach

b- the conservative approach

c- minimum regret

d- minimax regret

38. In assigning random numbers to probabilistic events in a simulation,

a- several events are associated with the same random number

b- every random number is associated with a particular event

c- every event is associated with the same random number

d-all of the above

39. A researcher wants to simulate sunny and rainy days in her town for a 3-week period. What is the minimum number of digits the student must obtain from a random number table for each observation if it rained on two-fifths of the days over the past several years at this time of the year? Assume that days can be classified historically as either sunny or rainy.

a- 1

b- 2

c- 3

d- all of the above.

40. The quantitative analysis approach requires

a- the manager's prior experience with a similar problem.

b- a relatively uncomplicated problem.

c- mathematical expressions for the relationships.

d- each of the above is true.

41. The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours of operation is observed to be the following:

Number of cars arriving Frequency

3 or less 0

4 10

0 30

6 70

7 50

8 40

9 or more 0

Based on the above frequencies, use two digit random numbers, start with random number 00 and determine the random number ranges for the data set given above.

42. The relationship d = 5000 - 25p describes what happens to demand (d) as price (p) varies. Here, price can vary between $10 and $50.

a. How many units can be sold at the $10 price? How many can be sold at the $50 price?

b. Model the expression for total revenue.

c. Consider prices of $20, $30, and $40. Which price alternative will maximize total revenue? What are the values for demand and revenue at this price?

43. A package of candy contains 12 brown, 5 red, and 8 green candies. You grab three pieces from the package. Give the sample space(set) of colors you could get. Order is not important.

44. There are two more assignments in a class before its end, and if you get an A on at least one of them, you will get an A for the semester. Your subjective assessment of your performance is

Event Probability

A on paper and A on exam .25

A on paper only .10

A on exam only .30

A on neither .35

a. What is the probability of getting an A on the paper?

b. What is the probability of getting an A on the exam?

c. What is the probability of getting an A in the course?

d. Are the grades on the assignments independent?

45. The high school GPA of applicants for admission to a college program are recorded and relative frequencies are calculated for the categories.

GPA F(x)

x < 2.0 .08

2.0 = x < 2.5 .12

2.5 = x < 3.0 .35

3.0 = x < 3.5 .30

3.5 = x

a. Complete the table to make this a valid probability distribution.

b. What is the probability an applicant's GPA will be below 3.0?

c. What is the probability an applicant's GPA will be 2.5 or above?

46. A calculus instructor uses computer aided instruction and allows students to take the midterm exam as many times as needed until a passing grade is obtained. Following is a record of the number of students in a class of 20 who took the test each number of times.

Number of Tests Students

1 10

2 7

3 2

4 1

a. Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition.

b. Find the expected value of the number of tests taken.

c. Compute the variance.

d. Compute the standard deviation.

47. Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores. Information on pricing, sales, and inventory costs has led to the following payoff table, in thousands.

Demand

Order Size Low Medium High

1 lot 12 15 15

2 lots 9 25 35

3 lots 6 35 60

a. What decision should be made by the optimist?

b. What decision should be made by the conservative?

c. What decision should be made using minimax regret?

48. The table shows both prospective profits and losses for a company, depending on what decision is made and what state of nature occurs. Use the information to determine what the company should do.

s1 s2 s3

d1 30 80 -30

d2 100 30 -40

d3 -80 -10 120

d4 20 20 20

a. if an optimistic strategy is used.

b. if a conservative strategy is used.

c. if minimax regret is the strategy.

49. The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

Minutes Relative Frequency

3 0.22

4 0.36

5 0.28

6 0.10

7 0.04

Using these random numbers, simulate the drying time for 5 processes: 0.53; 0.95; 0.97; 0.96; and 0.07.

50. Use a four period moving average to forecast attendance at future baseball games. Historical records show the attendance at ten consecutive baseball games as 5346, 7812, 6513, 5783, 5982, 6519, 6283, 5577, 6712, 7345.

#### Solution Preview

1. Random numbers generated by a mathematical process instead of a physical process are pseudorandom numbers.

True

False

Answer: True

Pseudorandom means that the "random" numbers are generated by a deterministic mathematical process, not by a fundamentally random physical process

2

In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution.

True

False

Answer: True

3. Two events that are independent cannot be mutually exclusive.

True

False

Answer: True

Definition of a mutually exclusive event: If event A happens, then event B cannot, or vice-versa.

Definition of independent events: The outcome of event A, has no effect on the outcome of event B.

So, if A and B are mutually exclusive, they cannot be independent. If A and B are independent, they cannot be mutually exclusive.

4. Experimental outcomes must occur as numerical values in order to define their probability distribution.

True

False

Answer: False

Heads and Tails that we obtain at the toss of a coin are not numerical values but we can calculate the probability of head and tail

5. A joint probability can have a value greater than 1.

True

False

Answer: False

Any probability cannot have a value greater than 1

6. A random variable that can take on any value along a line segment is a continuous random variable.

True

False

Answer: True

7. Sample information with an efficiency rating of 100% is perfect information.

True

False

Answer: True

8. States of nature should be defined so that one and only one will actually occur.

True

False

Answer: True

9. Time series methods base forecasts only on past values of the variables.

True

False

Answer: True

10. Random variations are movements that are not predictable and follow no pattern.

True

False

Answer: True

11. The field of decision science

a-concentrates on the use of quantitative methods to assist in decision making.

b-approaches decision making rationally, with techniques based on the scientific method.

c-is another name for management science and for operations research.

d-each of the above is true.

Answer: d-each of the above is true.

12. Identification and definition of a problem

a-cannot be done until alternatives are proposed.

b- is the first step of decision making.

c-is the final step of problem solving.

d-requires consideration of multiple criteria.

Answer: b- is the first step of decision making.

13

The appropriate decision criterion is dependent on

a-the risk personality of the decision maker.

b-the philosophy of the decision maker.

c-all of the above.

d-none of the above.

Answer: a-the risk personality of the decision maker.

14. Decision criteria

a-are the choices faced by the decision maker.

b-are the problems faced by the decision maker.

c-are the ways to evaluate the choices faced by the decision maker.

d-must be unique for a problem.

Answer: c-are the ways to evaluate the choices faced by the decision maker.

15

The term opportunity loss is most closely related to

a-maximin regret.

b-maximax regret.

c-minimax regret.

d-minimin regret.

Answer: c-minimax regret.

16. Which of the following is not a valid representation of a probability?

a-35%

b- 0

c-1.04

d- 3/8

Answer: c-1.04 (since it is greater than 1)

17

A ___________ probability distribution indicates the probability of r successes in n trials.

a- joint.

b- subjective.

c- marginal.

d- binomial.

Answer: d- binomial.

18

Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

Job Male (M) Female (F) Total

Administrative (AD) 110 10 110 10 120

Salaried staff (SS) 30 50 30 50 80

Hourly staff (HS) 60 40 60 40 100

If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member.

a- .1667

b-.5

c- .6

d- .625

e- .7

Answer: d- .625

Probability= 0.625 =50/80

19. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The complement of A is

a- all new customers.

b- all accounts fewer than 31 or more than 60 days past due.

c- all accounts from new customers and all accounts that are from 31 to 60 days past due.

d- all new customers whose accounts are between 31 and 60 days past due.

Answer: b- all accounts fewer than 31 or more than 60 days past due.

20. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The union of A and B is

a- all new customers.

b- all accounts fewer than 31 or more than 60 days past due.

c- all accounts from new customers and all accounts that are from 31 to 60 days past due.

d- all new customers whose accounts are between 31 and 60 days past due.

Answer: c- all accounts from new customers and all accounts that are from 31 to 60 days past due.

21. A numerical description of the outcome of an experiment is

a-a normal ...

#### Solution Summary

Answers and explanations to 50 Multiple choice questions on Random Numbers, Monte Carlo Process, Mutually Exclusive Events, Probability Distribution, Joint Probability, Perfect Information, Continuous Random variable, States of Nature, Decision Science, Opportunity Loss, complement, outcome of an experiment, repeated independent trials, options, decision tree, time series, seasonal components, smoothing methods, forecast errors, simulation, relative frequency