Which of the following formulas is a property of sampling distribution as defined by the...

The correct answer is A, σx̄ = σ / √n. This formula represents the standard deviation of the sampling distribution of the sample mean, often called the standard error of the mean. Under the central limit theorem, when repeated samples of size n are taken from a population, the distribution of the sample means approaches a normal distribution as sample size increases, and its spread is given by the population standard deviation divided by the square root of the sample size.

This concept is fundamental in the Measure Phase because Black Belts use sampling distributions to estimate population parameters, build confidence intervals, establish control limits for subgroup means, and perform hypothesis tests. The formula shows that as sample size increases, the variability of the sample mean decreases, meaning larger samples provide more precise estimates of the true population mean. Choice B is the arithmetic mean formula, not a central limit theorem property. Choice C is a regression equation, and Choice D is the chi-square test statistic formula. Therefore, the correct answer is A, because it directly describes a core property of the sampling distribution under the central limit theorem.