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 $3.50pm 0.21$. The same sample is used to set limits on anomalous $WWZ$ couplings.
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