= Solution
Use the preceding <electron density> as the line-of-sight mean, $L/c=2000\,\mathrm{yr}$, $\omega=2\pi(1.4\times10^9)\,\mathrm{s^{-1}}$ and $\Delta\omega=2\pi(4.0\times10^7)\,\mathrm{s^{-1}}$. Then
$$
\boxed{\Delta\tau\simeq8.4\times10^{-3}\,\mathrm s=8.4\,\mathrm{ms}.}
$$
This estimate corresponds to <dispersion measure> about $69.5\,\mathrm{pc\,cm^{-3}}$. A cloud density inferred from absorption need not equal the actual path average, so a real pulsar may differ even at the same distance.
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