  This Letter describes the current most precise measurement of the $WZ$
production cross section as well as limits on anomalous $WWZ$ couplings at a
center-of-mass energy of 1.96 TeV in proton-antiproton collisions for the
Collider Detector at Fermilab (CDF). $WZ$ candidates are reconstructed from
decays containing three charged leptons and missing energy from a neutrino,
where the charged leptons are either electrons or muons. Using data collected
by the CDF II detector (7.1 fb$^{-1}$ of integrated luminosity), 63 candidate
events are observed with the expected background contributing $8 \pm 1$ events.
The measured total cross section $\sigma (p \bar p \to WZ) =
3.93_{-0.53}^{+0.60}(\text{stat})_{-0.46}^{+0.59}(\text{syst}) $ pb is in good
agreement with the standard model prediction of $3.50\pm 0.21$. The same sample
is used to set limits on anomalous $WWZ$ couplings.
