Which of the following is guaranteed by the central limit theorem? The sampling

Question

Which of the following is guaranteed by the central limit theorem? The sampling distribution of certain classes of statistics will always be normally distributed regardless of the shape of the parent population. As sample size increases, the sampling distribution of x-bar will more closely approximate the normal curve when the sampled population has a nonnormal shape. The sampling distribution of x-bar is always normally distributed. The sampling distribution of x-bar will always have the same shape as the sampled population.

Explanation / Answer

the answer is - as sample size increases, the sampling distribution of x-bar will more closely approximate the normal curve when the sampled population has a non-normal shape.

because central limit theorem is a large sample criterion. it holds only when sample size is large. out of all the options only the above mentioned option has "as sample size increases". the other options have nothing to do with large sample property.

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