= Solution
The given calibration yields $M_V=-3.5\log_{10}50\simeq-5.946$. The <distance modulus> is $31.446$, giving $\boxed{d\simeq19.5\ \mathrm{Mpc}}$ if extinction is negligible. <Hubble's law> predicts $v_H\simeq1400$ km s$^{-1}$, compared with 1150 km s$^{-1}$ observed. The approximately $-250$ km s$^{-1}$ difference can be a line-of-sight <peculiar velocity> of the cluster and observer, together with distance-calibration uncertainties. The <local flow> need not follow a perfectly smooth expansion law.
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