Suppose μ = 50 and σ² = 100 for a population. In a sample where n = 100 is randomly taken, 90% of all possible sample means will fall between 49 and 51.

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The standard deviation of the sample mean (standard error) is σ/√n = 10/√100 = 1. Using the normal distribution, 90% of sample means fall within approximately 1.645 standard errors from the mean, which is not between 49 and 51.

Suppose μ = 50 and σ2 = 100 for a Population

Suppose μ = 50 and σ² = 100 for a Population