Question

what is the approximate distribution of the mean of a random sample size 36 frim a population whose mean and standard deviation are 20 and 12 respectively? why?

Answer 1

This distribution will be approximately normal. We know this from the central limit theorem which states that the distribution of the sampling means of any distribution is approximately normal, if the sample size is sufficiently large (greater than 30).

In our case, the sample size is greater than 30. Thus, the distribution will be normal.

The mean of such a distribution is equal to the population mean, and the standard deviation is equal to the population mean divided by the square root of the sample size.

Thus, new distribution mean= old distribution mean= 20

Thus, new distribution standard deviation= old distribution standard deviation= 12/sqrt(36)

= 12/6= 2