A payoff table is given as in each of your answer, show the work you relied upon

Question

A payoff table is given as in each of your answer, show the work you relied upon to reach your answer. What decision should be made using expected value, in which the probabilities are s_1=.5. S_2=.2. S_3=.3? What decision should be made by the conservative decision-maker? What choice should be made using the Hurwicz method, in which the coefficient of optimism (or realism) is .7? II. It is estimated that 20% of the athletes competing in a large tournament are users of an illegal drug to enhance performance. The test for this drug is 90% accurate. Determine the probability that an athlete who tests positive is actually a user. III. Scores on an endurance test for cardiac patients are normally distributed with mu= 185 and sigma = 10. a.What is the probability a patient will score above 195? b.What is the probability a patient will score below 175? IV. A manufacturer of low-budget television sets has a historical defective rate of ten percent.a. What is the probability that in a daily production run of 5 televisions, none will be defective? b. What is the probability that one or more will be defective? V. A manager must decide on the mix of products to produce for the coming week. Product A requires three minutes per unit for molding and two minutes per unit for painting. Product B requires two minutes per unit for molding and four minutes per unit for painting. There will be 400 minutes available for molding. 300 minutes for painting. Both products have profits of $1.00 per unit.

Explanation / Answer

Solution of question number III.

For the probability that a patient will score above 195, we have X 195

P ( X > 195 ) = P ( X > 195185 ) = P ( (X )/ > (195185)/10)

Since Z = x / = 195185/10 =1

now we have,

P ( X > 195 )=P ( Z > 1 )

Use the standard normal table for the value of z, now we have

P (Z > 1) = 0.1587

The probability that a patient will score above 195 is 0.1587

For the probability that a patient will score below 175, we have X 175

P ( X < 175 ) = P ( X < 175185 ) = P ( (X)/ < (175185)/ 10)

Since x/ = Z and 175185/10 = 1

Now we have,

P (X < 175)= P ( Z< 1)

Use the standard normal table for the value of z, now we have

P (Z < 1) = 0.1587

      The probability that a patient will score below 175 is 0.1587

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