Question

Which of the following is not a commonly used​ practice? Choose the correct answer below. A. If the original population is normally​ distributed, then for any sample size​ n, the sample means will be normally distributed. B. If the distribution of the sample means is normally​ distributed, and ngreater than​30, then the population distribution is normally distributed. C. The distribution of sample means gets closer to a normal distribution as the sample size n gets larger. D. If the original population is not normally distributed and ngreater than​30, the distribution of the sample means can be approximated reasonably well by a normal distribution.

Answer 1

Answer:

. B. If the distribution of the sample means is normally​ distributed, and greater than​30, then the population distribution is normally distributed

Answer 2

Using the Central Limit Theorem, it is found that the statement which does not represent a commonly used practice is:

B. If the distribution of the sample means is normally​ distributed, and n greater than​ 30, then the population distribution is normally distributed.

• The Central Limit Theorem establishes that, for a normally distributed random variable X,  the sampling distribution of the sample means with size n can be approximated to a normal distribution.
• For a skewed variable, the Central Limit Theorem can also be applied, as long as n greater than 30.

• From this, we have that no matter the distribution, for samples of at least 30, the distribution of the sample means is normal.
• If the underlying distribution is normal, the sample size is not important.
• However, we cannot infer anything about the population given the distribution of the sample means, thus, statement B is false.

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