Think about the following game: A fair coin is tossed 10 times. Each time the toss results in heads, you receive $10; for tails, you get nothing. What is the maximum amount you would pay to play the game? As a statistics student, you are aware that the game is a 10trial binomial experiment. A toss that lands on heads is defined as a success, and because the probability of a success is 0.5, the expected number of successes is 10(0.5) = 5. Since each success pays $10, the expected value of the game is 5($10) = $50. Suppose each person in a random sample of 1,536 adults between the ages of 22 and 55 is invited to play this game. Each person is asked the maximum amount they are willing to pay to play. (Data source: These data were adapted from Ben Mansour, Selima, Jouini, Elyes, Marin, Jean-Michel, Napp, Clotilde, & Robert, Christian. (2008). Are riskaverse agents more optimistic? A Bayesian estimation approach. Journal oprplied Econometrics, 23(6), 843860.) In Someone is described as \"risk neutra if the maximum amount he or she is willing to pay to play is equal to $50, the game's expected value. Suppose in this 1,536person sample, 34 people are risk neutral. Let p denote the proportion of the adult population aged 22 to 55 who are risk neutral and 1 p, the proportion of the same population who are not risk neutral. Use the sample results to estimate the proportion p. The proportion f; of adults in the sample who are risk neutral is V . The proportion 1 p of adults in the sample who are not risk neutral is V . You V conclude that the sampling distribution of i5 can be approximated by a normal distribution, because V The sampling distribution of has a mean V and an estimated standard deviation of V Distributions 0 1 2 3 Use the Distributions tool to develop a 99% confidence interval estimate of the proportion of adults aged 22 to 55 who are risk neutral. You can be 99% confident that the interval estimate LCL = to UCL = includes the population proportion p, the proportion of adults aged 22 to 55 who are risk neutral