Discussion
Sampling distribution of a statistic will be approximately normal when the sample size is ............
Answer: C
The sampling distribution is approximately normal when the sample size is sufficiently large.
By the central limit theorem, the sampling distribution of the mean (and of many other statistics) approaches a normal distribution as the sample size grows, whatever the shape of the population, provided its variance is finite. How large is large enough depends on the population; for most practical purposes a sample of 30 or more is taken as sufficient.
A small sample gives a normal sampling distribution only if the population itself is normal. 'Large' on its own is vaguer than the theorem's condition, which is that n is large enough for the approximation to hold, and 'optimum' sample size is a matter of cost and precision, not of the shape of the distribution.
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