alleryStart learning →A population that is already close to normal needs which sample size for the theorem to apply well?
ANone at all needed
BA relatively small one
CAn extremely large one
DAn infinite sample
Answer & Solution
Correct answer: B. A relatively small one
1. The required sample size depends on how far the population departs from normality.
2. If the original population is far from normal, then more observations are needed for the sample means or sums to be normal.
3. The converse follows: a nearly normal population needs comparatively few.
4. In the limiting case of an exactly normal population, even a sample of one is normally distributed.
5. Sampling is still needed, so the fourth option cannot be right.
_Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 7 'The Central Limit Theorem', sections 7.1-7.3_
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