  We present a measurement of the top-quark mass using the full data set of
Tevatron $\sqrt{s} = 1.96$ TeV proton-antiproton collisions recorded by the CDF
II detector, corresponding to an integrated luminosity of \invfb{8.7}. The
analysis uses events with one semileptonic $t$ or $\bar{t}$ decay, but without
detection of the electron or muon. We select events with significant missing
transverse energy and multiple jets. We veto events containing identified
electrons or muons. We obtain distributions of the top-quark masses and the
invariant mass of the two jets from $W$-boson decays from data and compare
these to templates derived from signal and background samples to extract the
top-quark mass and the energy scale of the calorimeter jets with {\it in situ}
calibration. A likelihood fit of the templates from signal and background
events to the data yields the top-quark mass, $\mtop =
\gevcc{\measStatSyst{173.93}{1.64}{0.87}}$. This result is the most precise
measurement to date of the mass of the top quark in this event topology.
