Whenever a sampled population is normally distributed or whenever the conditions of the Central Limit Theorem are fulfilled, the sample mean\(\style{font-family:Times New Roman;}{\overline x}\):

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is a consistent estimator of the population mean*μ *because the mean of the sampling distribution of the sample mean equals*μ*.

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is an efficient estimator of the population mean*μ *because the mean of the sampling distribution of the sample mean equals*μ*.

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is an unbiased estimator of the population mean*μ *because the mean of the sampling distribution of the sample mean equals*μ*.

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is a biased estimator of the population mean*μ *because the mean of the sampling distribution of the sample proportion equals*p*.