Solution
= Solution
Write the posterior mean and variance as
$$
m_n=\frac{n\overline X/\sigma^2+\mu/\nu^2}
{n/\sigma^2+1/\nu^2},
\qquad
v_n=\left(\frac n{\sigma^2}+\frac1{\nu^2}\right)^{-1}.
$$
The central 95 percent posterior credible interval is
$$
\boxed{m_n\mathbin{\pm}z_{0.975}\sqrt{v_n}}.
$$