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(Steps Shown) A variable of a population has mean μ and standard deviation σ. For a large sample size n, answer the following questions. Identify

Question: A variable of a population has mean \(\mu\) and standard deviation \(\sigma\). For a large sample size \(n\), answer the following questions.

  1. Identify the distribution of \(\bar{x}\).
  2. Does your answer to part (a) depend on \(n\) being large? Explain your answer.
  3. Identify the mean and the standard deviation of \(\bar{x}\).
  4. Does your answer to part (c) depend on the sample size being large? Why or why not?

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