I have the following questions as homework where I have to decide whether they are true or false. a) The standard deviation of the distribution of the sum of independent random variables is also called the central limit theorem. My guess for this question is that it should be true as the variance is the sum of all the variances of the number of variables involved and thus the standard deviation is the square root of the variance.
b) When a great many n random variables are drawn from a population that is normally distributed, the distribution of the sample mean will be normal regardless of the sample size n. For this part I don't really know how to work it out and decide if its true or false.
Can someone help me? Thank you.