Statistics - Interval Estimation - Proof

Question

Please tell me how to start on this proof or give me some kind of hint. Please click on this link to see the question

Show that if $X_1,X_2,\dots,X_n$ denotes an iid sample from $N(\mu,\sigma^2)$ and $\sigma^2$ is known, then the best $(1-\alpha)100\%$ confidence interval is $\Big(\bar{x} \mp z_\tfrac{\alpha}{2}\frac{\sigma}{\sqrt{n}}\Big).$

Thank you!

Original image: http://i.stack.imgur.com/MwfbG.jpg

Answer 1

Hint: $$ \frac{\bar{X}-\mu}{\sigma/\sqrt{n}}\sim\mathcal{N}(0,1), $$ where $\bar{X}=\frac{1}{n}\sum_{i=1}^n X_i$.