# Sampling Distributions Help

• February 2nd 2010, 02:56 PM
bobbe989
Sampling Distributions Help
Suppose that a random sample is to be taken from a normal distribution for which the value of the mean Theta is unknown and the standard deviation is 2. How large a random sample must be taken in order that
E[ |Xbar - theta|^2] <= 0.1 for ever possible value of theta?
• February 2nd 2010, 03:58 PM
matheagle
$E[|\bar X - \theta|^2]$ is the variance of X bar

and the variance of the sample mean is ${\sigma^2\over n}$

So set ${4\over n}\le .1$
• February 2nd 2010, 07:12 PM
bobbe989
Sampling Distributions Help - Again
I was just curious as to how this problem would be solved if the question were changed to :

E[ |Xbar - theta|]<= 0.1

Thanks