According to the Central Limit Theorem, as the sample size increases, the distribution of all possible sample means tends to be

According to the Central Limit Theorem, as the sample size increases, the distribution of all possible sample means tends to be

• A. Uniformly distributed
• B. Exponentially distributed
• C. Approximately normally distributed
• D. Skewed left

Answer: (C)

A key idea is that averaging many independent observations smooths out irregularities in the data. The Central Limit Theorem states that, for a large enough sample size, the distribution of the sample mean is approximately normal, with mean equal to the population mean and variance equal to the population variance divided by n. As n grows, this variance shrinks, so the sampling distribution becomes tighter around the true mean and looks bell-shaped. This holds even if the underlying population isn’t normally distributed, provided the variance is finite. Therefore, the distribution of all possible sample means tends to be approximately normally distributed as the sample size increases. It’s not uniform, not exponential, and not skewed left.

A key idea is that averaging many independent observations smooths out irregularities in the data. The Central Limit Theorem states that, for a large enough sample size, the distribution of the sample mean is approximately normal, with mean equal to the population mean and variance equal to the population variance divided by n. As n grows, this variance shrinks, so the sampling distribution becomes tighter around the true mean and looks bell-shaped. This holds even if the underlying population isn’t normally distributed, provided the variance is finite. Therefore, the distribution of all possible sample means tends to be approximately normally distributed as the sample size increases. It’s not uniform, not exponential, and not skewed left.