Solution
= Solution
{c}
The <sample mean> is exactly $N(\mu,\sigma^2/n)$, so $(\overline X-\mu)/(\sigma/\sqrt n)$ has the <standard normal distribution>. The given <quantile> gives probability $0.95$ to the interval $[-1.96,1.96]$. Inverting this <pivot> yields the exact $95\%$ <confidence interval>
$$
\boxed{\left[\overline X-1.96\frac\sigma{\sqrt n},\quad\overline X+1.96\frac\sigma{\sqrt n}\right].}
$$