Solution
= Solution
Since
$$
\overline X\sim N\left(\theta,\frac{\sigma^2}{n}\right),
$$
an exact 95 percent confidence interval is
$$
\boxed{
\overline X\mathbin{\pm}z_{0.975}\frac{\sigma}{\sqrt n}
},
\qquad z_{0.975}\simeq1.96.
$$
= Solution
Since
$$
\overline X\sim N\left(\theta,\frac{\sigma^2}{n}\right),
$$
an exact 95 percent confidence interval is
$$
\boxed{
\overline X\mathbin{\pm}z_{0.975}\frac{\sigma}{\sqrt n}
},
\qquad z_{0.975}\simeq1.96.
$$