
Statistical Consistency
My professor is not so clear on teaching in general, but especially not this section. The book isn't very helpful either. Hope you can help, the book suggests Chebyshev's inequality, but I'm not sure.
How large a sample must be taken from a normal pdf where E[Y] = 18 in order to guarantee that the estimator (mu) = Y(bar) = 1/n(Sum(Y)) has a 90% probability of lying somewhere in the interval 16,20? Assume that sigma = 5.
Thanks in advance for the help.

You need to solve $\displaystyle {\sigma\over\sqrt{n}}Z_{.05}=2$
I used confidence intervals to solve that, but directly it's
$\displaystyle .9=P(\bar X\mu<2)=P(Z<{2\over \sigma/\sqrt{n}})$
So, set $\displaystyle {2\over \sigma/\sqrt{n}}=Z_{.05}$, which better be the same.