Under the Central Limit Theorem, as the sample size increases, the distribution of the sample mean becomes approximately normal with mean equal to the population mean and standard deviation equal to

Under the Central Limit Theorem, as the sample size increases, the distribution of the sample mean becomes approximately normal with mean equal to the population mean and standard deviation equal to

• A. σX
• B. σX/√n
• C. σX√n
• D. σX^2/n

Answer: (B)

Under the Central Limit Theorem, the sampling distribution of the sample mean is approximately normal with its mean equal to the population mean and its spread given by the population standard deviation divided by the square root of the sample size. This quantity, σX/√n, is the standard error of the mean. As n grows, the standard error shrinks, so the distribution of the sample mean becomes more tightly clustered around the true mean. The other forms—using σX alone, multiplying by √n, or using σX^2/n—do not reflect how the variability of the sample mean behaves.

Under the Central Limit Theorem, the sampling distribution of the sample mean is approximately normal with its mean equal to the population mean and its spread given by the population standard deviation divided by the square root of the sample size. This quantity, σX/√n, is the standard error of the mean. As n grows, the standard error shrinks, so the distribution of the sample mean becomes more tightly clustered around the true mean. The other forms—using σX alone, multiplying by √n, or using σX^2/n—do not reflect how the variability of the sample mean behaves.