Question 1

Explain in 2-3 sentences why the Central Limit Theorem is important in statistics, is it because of which one:

1. For a large n, it says the population is approximately normal.
2. For any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.
3. For a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.
4. For any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Question 2

When your information about the distribution of your population is not sufficient and you don't know the distribution it follows. In this situation that is very common in real world, what is your recommendation for sampling to be allowed using the normality assumption for sample mean?