Decision Theory Final Exam Answer any four (4) of the following Roman numeral qu

Question

Decision Theory Final Exam Answer any four (4) of the following Roman numeral questions (I, 11, IIL, IV, v, VI Equal credit (25 points each). Do not answer more than four Roman numeral questions Make sure that for each answer you show your work I. Use the payoff table below in answering your questions. Again, be sure to show your work or explain how you reached your conclusion 250 300 100 450 200 -580 1000 700 1150 a. Which decision should be made by the conservative decision maker? b. Which decision should be made by the optimistic decision maker? Which decision should be made using the LaPlace version (equally likely probabilities) of expected value? d. Which decision should be made using minimax regret? eNot required. Extra credit -15 points - What is the expected value of perfect information? Il Scores on an endurance test for cardiac patients are normally distributed with - 185 and ?-14. . What is the probability a patient will score above 197? b. What is the probability a patient will score below 168? What is the probability a patient will score between 180 and 197? III. A manufacturer of television sets has a historical defective rate of fifteen percent. What is the probability that in a daily production run of 7 televisions, none will be defective? What is the probability that in a daily production run of 7 televisions, more than one will be defective? a. b. IV. A small company will be introducing a new line of lightweight bicycle frames to be made from special aluminum and steel alloys. The frames will be produced in two versions, a deluxe model and a professional model. The anticipated profit per unit is $10 for the deluxe, $15 for the professional. The number of pounds of aluminum alloy and steel alloy needed for the deluxe frame is 2 and 3, respectively. The number of pounds of aluminum alloy and steel alloy needed per professional frame is 4 and 2, respectively. A supplier delivers 100 pounds of the aluminum alloy and 80 pounds of the steel alloy weekly. What is the optimal weekly amount of each bicycle type the company should produce? Show your work.

Explanation / Answer

2)

mean = 185 , s = 14

a)
P(x > 197)

z = (x -mean)/s
= (197 - 185)/14
= 0.8571

P(x > 197) = P(z >0.8571) = 0.1957

b)

P(x < 168)

z = (x -mean)/s
= (168 - 185)/14
= -1.2143

P(x < 168) = P(z < -1.2143) = 0.1123

c)
P(180 < x < 197)

= P( ( 180 - 185)/14 < z < (197 - 185)/14)
= P(-0.3571 <z < 0.8571)
= 0.4438

3)

lambda = 0.15

Poisson's Distribution Formula:
P(X = x) = (e^-?) (?^x) / x!

a)
P(x = 0) = e^-0.15 * 0.15^0/0!
= 0.8607

b)
P(x > 1) = 1 - P(x =0)
= 1 - ( e^-0.15 * 0.15^0/0!)
= 0.1393

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.