Sppose you are sampling from a population with mean micro , Basic Statistics

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Sppose you are sampling from a population with mean micro

In given problem, what is the probability that the sample mean will be at least 1,000? Do you need to use the central limit theorem to answer this question? Explain.

Problem
Suppose you are sampling from a population with mean µ = 1,065 and standard deviation σ = 500. The sample size is n 100. What are the expected value and the variance of the sample mean X^‾?

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