Nancy is indifferent between a gamble that pays $625 with a probability of 20% and $100 with a probability of 80%, versus a sure payment of $169. She is also indifferent between another gamble that pays $169 with a probability of 50% and $49 with a probability of 50%, versus a sure payment of $100. Lastly, she is indifferent between a sure payment of $49 versus a gamble of receiving $100 with probability 0.625 and $4 with probability 0.375. Let (p1, P2, P3, P4, p5: 625, 169, 100.49. 4) represent a prospect (gamble) where p1, p2.p3.p4. and p5 represent the probabilities of the prizes $625, 169, 100, 49, and 4. respectively. a. Determine whether Nancy is risk-averse, risk-loving, or risk-neutral, based on her preferences. b. Rank the following four prospects according to Nancy's preferences. A: (0.2.0.2.0.2.0.2.0.2: 625, 169, 100,49,4) B: (0.4,0,0,0,0.6: 625, 169, 100, 49, 4) C:(0, 0.1, 0.8.0.0.1:625, 169, 100, 49, 4) D:(0.0.1.0.0.0: 625, 169, 100, 49, 4)