8. (12pts) A fair coin is flipped repeatedly. (a) (6pts) Suppose we hope that with probability...

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8. (12pts) A fair coin is flipped repeatedly. (a) (6pts) Suppose we hope that with probability at least 0.9 the frequency of heads showing up is between 0.4 and 0.6. Use Chebyshev's inequality to estimate at least how many times the coin should be flipped. (b) (6pts) Suppose we hope that with probability at least 0.95 the frequency of heads showing up is between 0.4 and 0.6. Use the central limit theorem to estimate at least how many times the coin should be flipped. 8. (12pts) A fair coin is flipped repeatedly. (a) (6pts) Suppose we hope that with probability at least 0.9 the frequency of heads showing up is between 0.4 and 0.6. Use Chebyshev's inequality to estimate at least how many times the coin should be flipped. (b) (6pts) Suppose we hope that with probability at least 0.95 the frequency of heads showing up is between 0.4 and 0.6. Use the central limit theorem to estimate at least how many times the coin should be flipped.