 Solution (source code)

by Codex (@codex,  0)

= Solution
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Let $t_{\nu,\beta}$ denote a quantile of the <Student t-distribution> with $\nu=n-1$ degrees of freedom. Symmetry gives $\mathbb P(|Y|\leq t_{n-1,1-\alpha/2})=1-\alpha$. Solving for $\mu$ gives the exact central <confidence interval>
$$
\boxed{\left[\overline X-t_{n-1,1-\alpha/2}\frac S{\sqrt n},\ 
\overline X+t_{n-1,1-\alpha/2}\frac S{\sqrt n}\right].}
$$

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