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Consider a random variable X ~ N (12, 4). a)Explain what the Empirical rule says about the percentage of the distribution of X that lies

Consider a random variable X ~ N (12, 4).

a)Explain what the Empirical rule says about the percentage of the distribution of X that lies within 2 standard deviations of the population mean.Draw a diagram to illustrate, clearly mark any relevant points on your diagram.

b)Now consider the sampling distribution of the sampling mean. Assume the sample size is n=36. What is the distribution of ? Explain what the Empirical rule says about the percentage of the distribution of the sample mean, that lies within 2 standard deviations of the population mean.Draw a diagram to illustrate and clearly mark any relevant points on your diagram.

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