How does the Central Limit Theorem influence the shape of the distribution of sample means?
- It states that all distributions will be skewed to the right.
- It states that as the sample size increases, the distribution of sample means will more closely approximate a normal distribution, regardless of the shape of the population distribution.
- The Central Limit Theorem does not influence the shape of the distribution.
- The Central Limit Theorem turns all distributions into uniform distributions.
The Central Limit Theorem (CLT) states that the distribution of sample means will tend towards a normal distribution as the sample size increases, regardless of the shape of the population distribution. Therefore, the CLT has a profound impact on the shape of the distribution, tending to 'normalize' it as sample size increases.
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