I would like some assistance with the following Quantitative Methods probability distribution questions

Determining the best payoff for each alternative and choosing the alternative with the "best of the best" is the approach called Select one: O a. expected monetary value O b. maximax O c. maximin O d. Laplace O e. minimax regretUse this information to answer the following questions. Consider the following Activity-On-Node (AON) PERT project. The three values that represent each activity's completion time (in days) correspond to an optimistic time, most likely time, and pessimistic time, respectively. 4-5-6 2-3-4 B D 3-4-5 4-5-6 A F 5-6-7 3-4-5 E Refer to the figure. What is the expected completion time of activity A? Select one: O a. 5 O b. 4 O c. 2.5 O d. 3 O e. 2.7Use this information to answer the following questions. Consider the following Activity-On-Node (AON) PERT project. The three values that represent each activity's completion time (in days) correspond to an optimistic time, most likely time, and pessimistic time, respectively. 4-5-6 2-3-4 B D 4-5-6 3-4-5 F A 5-6-7 3-4-5 E Refer to the figure. What deadline should be set to ensure a 99% probability that the project will be completed within the deadline date? Select one: O a, 20.56 days O b. 18.54 days O c. 18 days O d. 19 days O e. 19.45 daysFor any contimious random variable X, if a is some real constant, then PLY Q).Provide an appropriate response. The regression line for the given data is y = 0.449x - 30.27. Determine the residual of a data point for which x = 80 and y = 5. Temperature, x 72 85 91 90 88 98 75 100 80 Number of absences, y 3 10 10 8 15 15 5 Select one: O a. -0.65 O b. 108.025 O C. 5.65 O d. 10.65Provide an appropriate response. Express your answer as a simplified fraction unless otherwise noted, A county welfare agency employs 34 welfare workers who interview prospective food stamp recipients. Periodically, the supervisor selects, at random the forms completed by two workers to audit for illegal deductions. Unknown to the supervisor, eight of the workers have regularly been giving illegal deductions to applicants. Given that the first worker chosen has not been giving illegal deductions, what is the probability that the second worker chosen has been giving illegal deductions? Round to the nearest thousandth. Select one: O a. 0.212 O b. 0.206 O c. 0.235Provide an appropriate response. Express your answer as a simplified fraction unless otherwise noted. A county welfare agency employs 34 welfare workers who interview prospective food stamp recipients. Periodically, the supervisor selects, at random, the forms completed by two workers to audit for illegal deductions. Unknown to the supervisor, eight of the workers have regularly been giving illegal deductions to applicants. Given that the first worker chosen has not been giving illegal deductions, what is the probability that the second worker chosen has been giving illegal deductions? Round to the nearest thousandth. Select one: O a. 0:212 O b. 0.206 O c. 0.235 O d. 0.242Provide an appropriate response, Sixty-five percent of men consider themselves knowledgeable soccer fans. If 12 men are randomly selected, find the probability that exactly two of them will consider themselves knowledgeable fans Select one: 0 a. 0.65 O b. 0.001 O C. 0. 109 O d. 0.167Use the linear correlation coefficient given to determine the coefficient of determination, R . r=-0.38 Select one: O a. R = 14.44% O b. R = 61.64% 2 O C. R =-14.44% O d. R =-61.64%Provide an appropriate response. The coefficient of determination is the of the linear correlation coefficient. Select one: O a. square root O b. reciprocal O c. opposite O d. squareUse this information to answer the following questions. Consider the following payoff table that represents the profits earned for each alternative (A, B, and C) under the states of nature $1, $2, and 53. S1 A $60 $145 $120 B $75 $125 $110 C $95 $130 Refer to the payoff table. What is the expected value of perfect information (EVPI)? Assume P(S1) = 0.5 and P(S2) = 0.25. Select one: O a. $20 O b. $35 O G. $0 O d. $11.25 O e. $15