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P Ch ) = 4 PCt ) 1. Luke has an unfair coin. This coin is four times as likely to land on heads as on tails. Luke's arch-nemesis Cyrus is unaware that this coin is unfair, and so he agrees to flip this coin 16 times-each time, Luke will pay Cyrus a dollar if it lands on tails, and Cyrus will pay a dollar to Luke if the coin lands on heads. A loss or even a draw to Cyrus would be a catastrophe, so Luke wants to know his chances of taking home a profit. He doesn't have a computer or even a calculator to help him, but he never leaves home without his trusty Standard Normal Table. Let X, be the profit on each coin flip (which can be negative), let X be the sum Xi + ...+ X16, and let X be the average 16 X. (a) Find the expected value u = E(X,) for the profit on each coin flip. 1 = ECXi ) : (b) Find the standard error o = SE(X;) for the profit on each flip. (c) Luke sees profit when X > 0. Write this event in terms of X and in terms of Z, where Z is the normalization Z = - (d) With approximately what probability will Luke make a profit in this encounter? Answer to four decimal places using the standard normal table provided on bCourses