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Week Two Homework Assignment

1.    A student has an important exam coming up and is contemplating not studying for the exam in order to attend a party with his friends.  The student must earn a minimum score of 70% on the exam in order to successfully maintain his desired GPA.  The exam will consist of twenty multiple choice questions with four possible answers for each question.  Assuming correctly guessing the answer to a given question follows a binomial distribution, what is the probability that the student would earn less than the required minimum score of 70% on the exam based solely upon randomly guessing the correct answer for each question?

2.    The mean time to complete a construction project is 52 weeks with a standard deviation of 3 weeks.  Assuming the probability of completing the project follows a normal distribution, what is the probability of completing the project between 56 weeks and 64 weeks?

3.    Based upon the following data, what is the expected value of perfect information, assuming the probability of the state of nature that favors location A occurring is 0.50, the probability of the state of nature that favors location B occurring is 0.30, and the probability of the state of nature that favors neither location A nor location B occurring is 0.20.

Payoff Matrix

State of Nature Favors Alternative A    State of Nature Favors Alternative B    State of Nature Favors Neither Alternative A nor Alternative B
Alternative A    \$88     (\$5)    (\$5)
Alternative B    (\$8)    \$156     (\$8)
Alternatives A and B    \$80     \$151     (\$13)
Neither Alternative A
nor Alternative B    \$0     \$0     \$0

Note: The values in the preceding table are shown in millions of dollars.

4.    Based upon the following data,, what is the optimal decision using the expected opportunity loss decision rule, assuming the probability of the state of nature that favors alternative A occurring is 0.50, the probability of the state of nature that favors alternative B occurring is 0.30, and the probability of the state of nature that favors neither location A nor location B occurring is 0.20?

Payoff Matrix

State of Nature Favors Alternative A    State of Nature Favors Alternative B    State of Nature Favors Neither Alternative A nor Alternative B
Alternative A    \$88     (\$5)    (\$5)
Alternative B    (\$8)    \$156     (\$8)
Alternatives A and B    \$80     \$151     (\$13)
Neither Alternative A
nor Alternative B    \$0     \$0     \$0

Note: The values in the preceding table are shown in millions of dollars.

5.    Based upon using the expected monetary value decision rule and the following data, for what range of probability of the state of nature that favors alternative A occurring is selecting alternative A the optimal decision?  (Hint: Vary the probability of the state of nature that favors Alternative A occurring from 0.0 to 1.0 in increments of 0.01.)

Payoff Matrix

State of Nature Favors Alternative A    State of Nature Favors Alternative B
Alternative A    \$105.0    (\$5.0)
Alternative B    (\$25.0)    \$55.0
Alternatives A and B    \$80.0    \$50.0
Neither Alternative A
nor Alternative B    \$0.0    \$0.0

Note: The values in the preceding table are shown in millions of dollars.

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