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Which of the following is an appropriate statement of the central limit theorem? Select just one....

Which of the following is an appropriate statement of the central limit theorem? Select just one.

(1) The central limit theorem states that if you take a large random sample from a population and the data in the population are normally distributed, the data in your sample will be normally distributed.
  
(2) The central limit theorem states that if you take a large random sample from a population, the data in your sample will be normally distributed.

(3) The central limit theorem states that if you take many large random samples from a population and the data in the population are normally distributed, the sample means will be normally distributed.
  
(4) The central limit theorem states that if you take many large random samples from a population, the sample means will be normally distributed.

(5) The central limit theorem states that if you take many large random samples from a population and the data in the population are normally distributed, the data from the pooled samples will be normally distributed.
  
(6) The central limit theorem states that if you take many large random samples from a population, the data from the pooled samples will be normally distributed.

I believe the answer is two but I wanted to verify.

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Answer #1

Which of the following is an appropriate statement of the central limit theorem? Select just one.

correct option is

(2) The central limit theorem states that if you take a large random sample from a population, the data in your sample will be normally distributed.

Central Limit Therom states that the distribution of sample means approximates a normal distribution as the sample size becomes larger, assuming that all samples are identical in size and

regardless of the population distribution shape .

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