- Assume random variable x is from a normal distribution with mean µ = 20 and standard deviation σ = 5, find the following probabilities:

a. P(14.735 £ x £ 30.325)

b. P(9.225 £ x £ 35)

c. P(x £ 27.5)

d. P(25 £ x £ 29.175)

- Given the profit payoff table below:
Decision alternative-d1State of Nature s1

s1 s2 s3 s4

d1 12 9 10 4

d2 14 10 8 6

d3 9 12 15 11

d4 8 10 11 13

Suppose the manager has no probability information, what is the decision recommendation for him using the optimistic, conservative, and min-max regret approach?