Sample means are approximately normally distributed when n 3

Sample means are approximately normally distributed when n 30. The Central Limit Theorem is used to argue that distributions frequently arising in nature are normal or approximately normal. The standard deviation of a sampling distribution of means is 1 divided by the square root of n (the sample size) tunes the standard deviation of the original population. A distribution of sample sums may not be normally distributed.

Solution

OPTION 2 IS INCORRECT. [ANSWER]

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This is so because the central limit theorem does not say anything about the distributions being normal themselves. It says that the SAMPLING DISTRIBUTION OF THE MEANS are approximately normally distributed regardless of the underlying distribution.