= Solution
In an <Einstein-de Sitter universe>, $H(z)=100h(1+z)^{3/2}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$. At the cloud's approximate epoch $z_*=3$, $H=800h\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, and $\delta z=0.1$ corresponds to $\delta v\simeq7500\,\mathrm{km\,s^{-1}}$. Therefore
$$
\boxed{d_{cq}\simeq9.4\,h^{-1}\mathrm{Mpc}\quad\text{proper},\qquad \Delta\chi\simeq37.5\,h^{-1}\mathrm{Mpc}\quad\text{comoving}.}
$$
Choosing the midpoint $z_*=3.05$ instead gives $9.1\,h^{-1}\mathrm{Mpc}$ proper. Thus the intended approximate proper distance is about \b[$9\,h^{-1}\mathrm{Mpc}$]; the small variation reflects the epoch choice in the local expansion, not a factor-of-four physical discrepancy. For example the exact comoving separation is $2cH_0^{-1}[(1+z_c)^{-1/2}-(1+z_q)^{-1/2}]$, whose conversion at the midpoint agrees with that estimate.
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