No, the point is that chebyshev's is a very weak inequality in this setting.
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.