Discussion
The Central Limit theorem assures that the mean sample distribution is ..............
Answer: D
The answer is that the sampling distribution of the mean approaches normal as the sample size increases.
The central limit theorem states that, whatever the shape of the population (provided it has a finite variance), the distribution of the sample mean becomes closer and closer to a normal distribution as the sample size grows, with mean equal to the population mean and standard error σ/√n.
It is not 'always normal': for small samples from a non-normal population it is not. Even for large samples the theorem gives an approximation that improves with n, not exact normality, and no fixed size such as 1,000 is required; samples of about 30 are usually treated as large enough.
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