Suppose X is a single observation from normal (μ,1). find 95% confidence interval for μ?
(use maximum likelihood estimate)
you can plug into the usual formula with n=1 and X=sample mean
or solve for moo....
$\displaystyle .95=P(-1.96<X-\mu<1.96)$
and you need not make it symmetric, but that's all that people are doing these days...
(X-1.96,X+1.96) is the answer in that case.