How do you apply the Central Limit Theorem to demonstrate that the sampling distribution of the sample mean approximates a normal distribution, even when the sample data is not normally distributed?

The Central Limit Theorem (CLT) states that the sampling distribution of the sample mean will approximate a normal distribution as the sample size becomes large, regardless of the population’s distribution. This approximation improves with larger sample sizes, typically n > 30. Therefore, even if the sample data is not normally distributed, the sample mean will tend to follow a normal distribution due to the CLT.

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