The Central Limit Theorem describes the behavior of:

The Central Limit Theorem describes the behavior of:

• A. individual numeric observations in a population.
• B. the distribution of all possible sample variances as the sample size increases.
• C. the distribution of all possible sample standard deviations as the sample size increases.
• D. the distribution of all possible sample means as the sample size increases.

Answer: (D)

The Central Limit Theorem focuses on the distribution of the sample mean when you take repeated samples from a population. As the sample size grows, the distribution of those sample means becomes approximately normal, even if the underlying population isn’t normal. This normal distribution has a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (sigma/sqrt(n)). In other words, it’s about all possible sample means you could obtain from repeated sampling, not about individual observations or about the distributions of variances or standard deviations across samples.

The Central Limit Theorem focuses on the distribution of the sample mean when you take repeated samples from a population. As the sample size grows, the distribution of those sample means becomes approximately normal, even if the underlying population isn’t normal. This normal distribution has a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (sigma/sqrt(n)). In other words, it’s about all possible sample means you could obtain from repeated sampling, not about individual observations or about the distributions of variances or standard deviations across samples.