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What are the requirements on sampling and the population so that the distribution of sample means is approximately normal? How do you calculate the mean

  1. What are the requirements on sampling and the population so that the distribution of sample means is approximately normal?
  2. How do you calculate the mean and standard deviation of the sampling distribution for sample means?
  3. What is the effect of increasing sample size on the sampling distribution and what does this mean in terms of the central limit theorem?
  4. Why is the standard deviation of the sampling distribution smaller than the standard deviation of the population from which it came?

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