Week Two Homework Assignment Linear Regression Complete Solution
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. Suppose the student knows in advance that the exam will consist of twenty multiple choice questions with four possible answers for each question. Answer questions 1-3 using the preceding information and modeling this situation as a binomial distribution.
The mean time required to complete a certain type of construction project is 52 weeks with a standard deviation of 3 weeks. Answer questions 4-7 using the preceding information and modeling this situation as a normal distribution.
Customers arrive at a supermarket check-out counter with an average arrival rate of 9 customers per hour. Answer questions 8-10 using the preceding information and modeling this situation as a Poisson distribution.
A local commuter bus service advertises that buses run every twelve minutes along a certain route. Answer questions 11and 12 using the preceding information and modeling this situation as an exponential distribution.
Scores for a certain exam follow a normal distribution with a mean of 87 and a standard deviation of 4. Answer questions 13and 14 using the preceding information.
Use the following data set and assumptions to create payoff and regret matrices in order to answer questions 15 through 18.
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Assume that there are four collectively exhaustive alternatives from which you must choose prior to knowing the actual state of nature that will occur.
Assume that there are two collectively exhaustive states of nature that could occur.
Assume that the estimated costs associated with selecting a given alternative must be incurred prior to knowing which state of nature will actually occur.
Use the payoff and regret data provided in the following payoff and regret matrices to answer questions 19 through 22.
Payoff Matrix
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States of Nature |
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Alternatives |
State of Nature Favors A |
State of Nature Favors B |
State of Nature Favors Neither A nor B |
A |
$88 |
($5) |
($5) |
B |
($8) |
$156 |
($8) |
A and B |
$80 |
$151 |
($13) |
Neither A nor B |
$0 |
$0 |
$0 |
Note: The values in the preceding table are shown in millions of dollars.
Regret Matrix
States of Nature |
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Alternatives |
State of Nature Favors A |
State of Nature Favors B |
State of Nature Favors Neither A nor B |
A |
$0 |
$161 |
$5 |
B |
$96 |
$0 |
$8 |
A and B |
$8 |
$5 |
$13 |
Neither A nor B |
$88 |
$156 |
$0 |
Note: The values in the preceding table are shown in millions of dollars.
For questions 23 through 25, use the following payoff matrix data to create a sensitivity analysis data table that summarizes the expected monetary value for each possible alternative relative to the probability of the state of nature that occurs favoring Alternative A being varied from 0.0 to 1.0 in increments of 0.01.
Payoff Matrix
Alternatives |
State of Nature 1 (Favors A) |
State of Nature 2 (Favors B) |
A |
$105.0 |
($5.0) |
B |
($25.0) |
$55.0 |
A and B |
$80.0 |
$50.0 |
Neither A nor B |
$0.0 |
$0.0 |
Week Two Homework Assignment - Linear Regression Complete Solution
as a binomial distribution.
What is the probability that the student will successfully earn exactly the required minimum score of 70% on the exam based solely upon randomly guessing th...
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