Intermediate Microeconomics question

5. (10 marks) 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 indiffemnt between a sure payment of $49 versus a gamble of receiving $100 with probability 0.625 and $4 with probability 0.375. Let (pl, 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 riskaverse, riskloving, or riskneutral, 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)