Question 1

Blanca has her choice of either a certain income of $20,000 or a gamble with a 0.5 probability of $10,000 and a 0.5 probability of $30,000. The expected value of the gamble:
A) is less than $20,000.
B) is $20,000.
C) is greater than $20,000.
D) cannot be determined with the information provided.

Accepted Answer

The expected value of the gamble is calculated as (0.5 * $10,000) + (0.5 * $30,000) = $5,000 + $15,000 = $20,000, which is equal to the certain income of $20,000.

Question 2

Scenario 5.4:
Suppose an individual is considering an investment in which there are exactly three possible outcomes, whose probabilities and payoffs are given below:
  The expected value of the investment is $25. Although all the information is correct, information is missing.
-Refer to Scenario 5.4. What is the standard deviation of the investment?
A) 0
B) 16.58
C) 56.12
D) 90.14
E) none of the above

Accepted Answer

The answer of Scenario 5.4:
Suppose an individual is considering an...

Question 3

Scenario 5.4:
Suppose an individual is considering an investment in which there are exactly three possible outcomes, whose probabilities and payoffs are given below:
  The expected value of the investment is $25. Although all the information is correct, information is missing.
-Refer to Scenario 5.4. What is the deviation of outcome A?
A) 30
B) 50
C) 75
D) 100

Accepted Answer

To calculate the deviation of Outcome A, we need to subtract the expected value from the payoff of Outcome A and take its absolute value.

Deviation of Outcome A = |$20 - $25| = $5

The best choice depends on the individual's risk tolerance and investment goals. If they are risk-averse, they may choose Outcome B with a lower potential payoff but a higher probability of success. If they are more risk-tolerant, they may choose Outcome C with a higher potential payoff but a lower probability of success. It ultimately comes down to the individual's personal preferences and investment strategy.

Question 4

Assume that one of two possible outcomes will follow a decision. One outcome yields a $75 payoff and has a probability of 0.3; the other outcome has a $125 payoff and has a probability of 0.7. In this case the expected value is:
A) $85.
B) $60.
C) $110.
D) $35.

Accepted Answer

To calculate the expected value, we use the formula: 
Expected value = (probability of outcome 1 x value of outcome 1) + (probability of outcome 2 x value of outcome 2)

In this case, the expected value is:
(0.3 x 75) + (0.7 x 125) = 22.5 + 87.5 = $110

Therefore, the best choice is to choose the option with the higher expected value, which is $110.

Question 5

Table 5.4
 
-Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, then in absolute value:
A) W = X = $10.
B) W = X = $20.
C) W = Y = $100.
D) W = Y = $200.
E) W = Y = $300.

Accepted Answer

W = $10 and X = $10 because the expected value of Job A is $10, and the expected value of outcomes 1 and 2 are both $10.

Question 6

Scenario 5.4:
Suppose an individual is considering an investment in which there are exactly three possible outcomes, whose probabilities and payoffs are given below:
  The expected value of the investment is $25. Although all the information is correct, information is missing.
-Refer to Scenario 5.4. What is the payoff of outcome C?
A) -150
B) 0
C) 25
D) 100
E) 150

Accepted Answer

Outcome C has a payoff of -150.

Question 7

Scenario 5.4:
Suppose an individual is considering an investment in which there are exactly three possible outcomes, whose probabilities and payoffs are given below:
  The expected value of the investment is $25. Although all the information is correct, information is missing.
-Refer to Scenario 5.4. What is the probability of outcome B?
A) 0
B) -0.5
C) 0.5
D) 0.4
E) 0.2

Accepted Answer

Probabilities must be between 0 and 1, and 0.5 is a valid probability value.

Question 8

Table 5.4
 
-Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, and if at Job B the $20 outcome occurs with probability .1, and the $50 outcome occurs with probability .9, then:
A) Job A is safer because the difference in the probabilities is lower.
B) Job A is riskier only because the expected value is lower.
C) Job A is riskier because the standard deviation is higher.
D) Job B is riskier because the difference in the probabilities is higher.
E) There is no definite way given this information to tell how risky the two jobs are.

Accepted Answer

Job A is considered riskier because the standard deviation, which measures the spread or variability of outcomes, is higher when outcomes are equally likely compared to Job B, where one outcome is much more likely than the other.

Question 9

Table 5.4
 
-Refer to Table 5.4. If at Job B the $20 outcome occurs with probability .2, and the $50 outcome occurs with probability .8, then the standard deviation of payoffs at Job B is nearest which value?
A) $10
B) $12
C) $20
D) $35
E) $44

Accepted Answer

To calculate the standard deviation of payoffs at Job B, we first need to calculate the expected payoff:

Expected payoff = (probability of $20 outcome x $20) + (probability of $50 outcome x $50)
Expected payoff = (.2 x 20) + (.8 x 50)
Expected payoff = $44

To calculate the standard deviation, we need to find the variance first:

Variance = [(probability of $20 outcome x ($20 - expected payoff)^2) + (probability of $50 outcome x ($50 - expected payoff)^2)]
Variance = [(.2 x (20-44)^2) + (.8 x (50-44)^2)]
Variance = [(.2 x 576) + (.8 x 36)]
Variance = 146.4

Standard deviation = square root of variance = sqrt(146.4) = 12

Therefore, the standard deviation of payoffs at Job B is nearest to $12. Answer choice B is correct.

Question 10

An investment opportunity has two possible outcomes. The expected value of the investment opportunity is $250. One outcome yields a $100 payoff and has a probability of 0.25. What is the payoff of the other outcome?
A) -$400
B) $0
C) $150
D) $300
E) none of the above

Accepted Answer

The expected value is calculated as (0.25 * $100) + (0.75 * X) = $250. Solving for X gives X = $300.

Question 11

An investment opportunity has two possible outcomes, and the value of the investment opportunity is $250. One outcome yields a $100 payoff and has a probability of 0.25. What is the probability of the other outcome?
A) 0
B) 0.25
C) 0.5
D) 0.75
E) 1.0

Accepted Answer

The total probability of all possible outcomes must equal 1. Therefore, the probability of the other outcome is 1 - 0.25 = 0.75.

Question 12

The expected value is a measure of:
A) risk.
B) variability.
C) uncertainty.
D) central tendency.

Accepted Answer

The expected value is a measure of central tendency, specifically the average outcome that is expected if the process is repeated many times. It is not a measure of risk, variability, or uncertainty, although it can be used to help assess those factors.

Question 13

The expected value of a project is always the:
A) median value of the project.
B) modal value of the project.
C) standard deviation of the project.
D) weighted average of the outcomes, with probabilities of the outcomes used as weights.

Accepted Answer

The expected value of a project is the weighted average of the outcomes, with probabilities of the outcomes used as weights. This gives a more accurate representation of the potential value of the project than using the median or mode. Standard deviation is a measure of risk, not the expected value.

Question 14

Table 5.4
 
-Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, then the standard deviation of payoffs at Job A is:
A) $1.
B) $10.
C) $40.
D) $50.
E) $60.

Accepted Answer

To find the standard deviation of payoffs, we first need to calculate the expected value or mean payoff. Since outcomes 1 and 2 are equally likely at Job A, the expected value of payoff is the average of those two outcomes:
Expected value = (1 + 2) / 2 = $1.50

Next, we need to calculate the variance, which is the average of the squared deviations from the mean:
Variance = [(1 - 1.5)^2 + (2 - 1.5)^2] / 2 = 0.25

Finally, the standard deviation is the square root of the variance:
Standard deviation = sqrt(0.25) = $0.50

Therefore, the best choice is B, $10, since it is the closest option to the calculated standard deviation.

Question 15

Scenario 5.4:
Suppose an individual is considering an investment in which there are exactly three possible outcomes, whose probabilities and payoffs are given below:
  The expected value of the investment is $25. Although all the information is correct, information is missing.
-Refer to Scenario 5.4. What is the variance of the investment?
A) -75
B) 275
C) 3,150
D) 4,637.50
E) 8,125

Accepted Answer

The answer of Scenario 5.4:
Suppose an individual is considering an...

Question 16

Which of the following is NOT a generally accepted measure of the riskiness of an investment?
A) Standard deviation
B) Expected value
C) Variance
D) none of the above

Accepted Answer

Expected value is not a measure of riskiness, but rather a measure of potential return. Standard deviation and variance are both commonly used measures of riskiness, as they capture the variability of returns around the expected value.

Question 17

Table 5.4
 
-Refer to Table 5.4. If at Job B the $20 outcome occurs with probability .2, and the $50 outcome occurs with probability .8, then in absolute value:
A) Y = Z = $6.
B) Y = Z = $24.
C) Y = Z = $35.
D) Y = $24; Z = $6.
E) Y = $6; Z = $24.

Accepted Answer

From the table, we can see that the outcome of Job B is either $20 or $50. Since the probabilities are given, we can calculate the expected value of each outcome as follows:

Expected value of $20 outcome = $20 x 0.2 = $4
Expected value of $50 outcome = $50 x 0.8 = $40

The total expected value of Job B is the sum of the expected values of the outcomes, which is:

Total expected value = $4 + $40 = $44

To find the values of Y and Z, we need to compare the expected value of Job B to the expected value of the bundle.

Expected value of the bundle = Y x 0.3 + Z x 0.7

Since the bundle consists of five jobs, each with an equal probability of 0.2, we know that the expected value of the bundle must be:

Expected value of the bundle = (Y + Z)/2

Setting these two expressions for the expected value equal to each other and solving for Y and Z gives:

(Y + Z)/2 = $44
Y + Z = $88

Since Y and Z are equal in absolute value, they must each be $44/2 = $22. However, the answer choices only give options in absolute value, so we choose the pair with one value of $24 and one value of $6:

Y = $24; Z = $6  (or vice versa)

Question 18

An investment opportunity is a sure thing; it will pay off $100 regardless of which of the three possible outcomes comes to pass. The variance of this investment opportunity:
A) is 0.
B) is 1.
C) is 2.
D) is -1.
E) cannot be determined without knowing the probabilities of each of the outcomes.

Accepted Answer

Since the investment opportunity will always pay off $100 regardless of which outcome occurs, there is no variability or risk involved. Therefore, the variance of the investment opportunity is 0.

Question 19

The weighted average of all possible outcomes of a project, with the probabilities of the outcomes used as weights, is known as the:
A) variance.
B) standard deviation.
C) expected value.
D) coefficient of variation.

Accepted Answer

The expected value is the weighted average of all possible outcomes, which takes into account the probabilities of each outcome occurring. The variance and standard deviation measure the spread of the data, but do not take into account the probabilities of each outcome. The coefficient of variation is a measure of relative variability, calculated as the standard deviation divided by the mean, and is not directly related to the probabilities of outcomes in a project.

Question 20

The variance of an investment opportunity:
A) cannot be negative.
B) has the same unit of measure as the variable from which it is derived.
C) is a measure of central tendency.
D) is unrelated to the standard deviation.

Accepted Answer

The variance of an investment opportunity cannot be negative because it is a measure of the variability of returns and variability cannot be negative.

Quiz 5: Uncertainty and Consumer Behavior

Blanca has her choice of either a certain income of $20,000 or a gamble with a 0.5 probability of $10,000 and a 0.5 probability of $30,000. The expected value of the gamble:

Assume that one of two possible outcomes will follow a decision. One outcome yields a $75 payoff and has a probability of 0.3; the other outcome has a $125 payoff and has a probability of 0.7. In this case the expected value is:

Table 5.4 -Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, then in absolute value:

Table 5.4 -Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, and if at Job B the $20 outcome occurs with probability .1, and the $50 outcome occurs with probability .9, then:

Table 5.4 -Refer to Table 5.4. If at Job B the $20 outcome occurs with probability .2, and the $50 outcome occurs with probability .8, then the standard deviation of payoffs at Job B is nearest which value?

An investment opportunity has two possible outcomes. The expected value of the investment opportunity is $250. One outcome yields a $100 payoff and has a probability of 0.25. What is the payoff of the other outcome?

An investment opportunity has two possible outcomes, and the value of the investment opportunity is $250. One outcome yields a $100 payoff and has a probability of 0.25. What is the probability of the other outcome?

The expected value is a measure of:

The expected value of a project is always the:

Table 5.4 -Refer to Table 5.4. If outcomes 1 and 2 are equally likely at Job A, then the standard deviation of payoffs at Job A is:

Which of the following is NOT a generally accepted measure of the riskiness of an investment?

Table 5.4 -Refer to Table 5.4. If at Job B the $20 outcome occurs with probability .2, and the $50 outcome occurs with probability .8, then in absolute value:

An investment opportunity is a sure thing; it will pay off $100 regardless of which of the three possible outcomes comes to pass. The variance of this investment opportunity:

The weighted average of all possible outcomes of a project, with the probabilities of the outcomes used as weights, is known as the:

The variance of an investment opportunity: