Question

To estimate the mean of a population, what do you do if you do not know the distribution of the population? (you should explain what theorem you use and how this theorem is helpful).

Answer 1

The distribution of the population is not known to us. In order to estimate the population mean, we need to draw a random sample from the population. The sample size should be large enough (at least mlre than 30). Also the sample should be drawn randomly.

Hence, by central limit theorem, the sample mean will converge to the population mean as the sample size n increases. Hence, the sample mean if sufficiently large sample will give an estimate of the population mean.