The Central Limit Theorem tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases. This fundamental theorem is a cornerstone of statistics, emphasizing that the sampling distribution of the mean becomes approximately normal, regardless of the population's shape, provided the sample size is sufficiently large.

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Related Questions:

1. What conditions are necessary for the Central Limit Theorem to apply?
2. How does sample size affect the accuracy of the Central Limit Theorem?
3. Can you explain the significance of the Central Limit Theorem in hypothesis testing?
4. What happens to the standard error as the sample size increases?
5. How does the Central Limit Theorem relate to the law of large numbers?

Tip: A common guideline is that a sample size of 30 or more is typically sufficient for the Central Limit Theorem to hold, but smaller sizes may suffice if the population distribution is not highly skewed.