If \(q(X,0)\sim N(0,1)\) is the Pivotal function for θ,

This implies the 95% confidence interval can be given by

\(P(Z_{0.025})\)

Now simplify this expression until an expression of this kind is obtained

\(P(Z_{0.025}\times A<0\)

Where A and B are constants.

For example, for the pivotal function formed in (b), Confidence Interval can be given by

\(P(\overline{x}+Z_{0.025}\times\frac{\sigma}{n}<0<\overline{x}+Z_{0.975}\times\frac{\sigma}{n})=0.95\)

The confidence interval is

\((\overline{x}-1.96\times\frac{\sigma}{n}, \overline{x}+1.96\times \frac{\sigma}{n})\)