= Solution
For large $|\overline x|$, the supplied normal-tail approximation gives
$$
p(\overline x)
\sim\frac1{5\sqrt{2\pi}\,|\overline x|}
e^{-50\overline x^2}.
$$
Meanwhile,
$$
q(\overline x)
\sim\sqrt{101}
\exp\left(-\frac{5000}{101}\overline x^2\right).
$$
Since $5000/101<50$, the posterior point-null probability decays more slowly. Therefore, for sufficiently large $|\overline x|$,
$$
\boxed{q(\overline x)>p(\overline x)}.
$$
This reversal is the <Jeffreys-Lindley paradox for a Gaussian point null>.
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