Question

# The Central Limit Theorem says that when sample size n is taken from any population with...

The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are true?

1. The distribution of the sample mean is approximately Normal.
2. The standard deviation is equal to that of the population.
3. The distribution of the population is exactly Normal.
4. The distribution is biased.

Solution:

Given: The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, then the distribution of the sample mean is approximately Normal.

thus first options is correct.

In this case  standard deviation of sample means = which is not equal to population standard deviation, thus second option is not correct.

Since population distribution is unknown, we can not say distribution is exactly Normal. Thus third option is not correct.

We either say distribution is normally or approximately Normal or Non-normal, so fourth option is not correct.

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