Question 3 Consider flipping a (biased) coin for which the probability of head is p. The fraction of heads after n independent tosses is Xm. (a) so that approximately P(0.5 < Xn < 0.7) > 0.95? Hint: If Z ~ N(0, 1), then P(-1.96 < Z < 1.96) = 0.95. Suppose p = 0.6. Using the Central Limit Theorem, how large should n be Note: Compare your result here with Question 4(b) in Homework 1, where you calculated such n using Chebyshev's inequality. Are the n's you obtained the same/different? Which n is greater? How would you understand/interpret this difference? (Something to think about; need to answer this in your solution.)

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