Connie's Utility Depends Upon Her Income

Essay

Connie's utility depends upon her income. Her utility function is U = I^1/2. She has received a prize that depends on the roll of a pair of dice. If she rolls a 3, 4, 6 or 8, she will receive $400. Otherwise she will receive $100.
a. What is the expected payoff from this prize? [Hint: The probability of rolling a 3 is 1/18, the probability of rolling a 4 is 3/36, the probability of rolling a 6 is 5/36, and the probability of rolling an 8 is 5/36.]
b. What is the expected utility from this prize?
c. Connie is offered an alternate prize of $169 (no dice roll is required). Will she accept the alternate prize or roll the dice?
d. What is the minimum payment that Connie will accept to forego the roll of the dice?