The Central Limit Theorem is applicable provided the sample size is sufficiently large.

The Central Limit Theorem is applicable provided the sample size is sufficiently large.

• A. the population is normally distributed
• B. the sample size is exactly 30
• C. the population variance equals 0
• D. the sample size is sufficiently large

Answer: (D)

The central concept being tested is that the sampling distribution of the mean becomes approximately normal as the sample size grows, regardless of the population's shape, as long as the variance is finite and the observations are independent. This is why the idea that the Central Limit Theorem is applicable when the sample size is sufficiently large holds true. If the population is already normal, you still get a normal sampling distribution for the mean, but you don’t rely on a fixed n; the key point is that, in general, a large enough sample size makes the normal approximation reliable. A specific number like 30 is not a universal rule, and having a population variance of zero isn’t meaningful for establishing the normality of the sampling distribution.

The central concept being tested is that the sampling distribution of the mean becomes approximately normal as the sample size grows, regardless of the population's shape, as long as the variance is finite and the observations are independent. This is why the idea that the Central Limit Theorem is applicable when the sample size is sufficiently large holds true. If the population is already normal, you still get a normal sampling distribution for the mean, but you don’t rely on a fixed n; the key point is that, in general, a large enough sample size makes the normal approximation reliable. A specific number like 30 is not a universal rule, and having a population variance of zero isn’t meaningful for establishing the normality of the sampling distribution.