Let be independent, normal random variables, each with mean and variance .

a) Find the density function of .

Solution to (a): So, U is normally distributed with mean and variance .

b) If and , what is the probability that the sample mean, , takes on a value that is within one unit of the population mean, ? That is, find .

So, the way I have been trying to solve it is by finding the probability , but I have had no luck. I get the feeling it is right in front of me. Should I use Tchebysheff's theorem?

Thanks for the help

oh, and is supposed to represent y with a bar (_) over it...not sure how to do that.