Suppose μ = 80 and σ² = 400 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall above 76.71.

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Quizplus · Accepted Answer

This statement is true because the sample mean follows a normal distribution with mean μ and standard deviation σ/√n, where n is the sample size. Using the given population parameters, we can calculate that the standard deviation of the sample mean is σ/√n = 20. Therefore, a sample mean of 76.71 is 1.645 standard deviations below the population mean of 80. This corresponds to the 5th percentile of the normal distribution, and since the distribution is symmetric, 95% of all possible sample means will fall above this value.

Suppose μ = 80 and σ2 = 400 for a Population

Suppose μ = 80 and σ² = 400 for a Population