1.    Suppose that a researcher is interested in estimating the population mean (Miu_X) of a population with the sample average estimator, X_bar. The population has a population standard deviation of Sigma_X.The question that the research has is: “How large should my sample size be?” You help her out and tell her the following:  “Your sample size (n) should be such that there is a 95% chance that the X_bar will be within +/-10% away from the Miu_X.”Based on this information, please derive a mathematical expression for the sample size (n) as a function of Miu_X and Sigma_X.

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