We present a measurement of the ratio of the top-quark branching fractions R=B(t→Wb)/B(t→Wq), where q represents quarks of type b, s, or d, in the final state with a lepton and hadronic jets. The measurement uses √s=1.96  TeV proton-antiproton collision data from 8.7  fb−1 of integrated luminosity collected with the Collider Detector at Fermilab during Run II of the Tevatron. We simultaneously measure R=0.94±0.09 (stat+syst) and the tt production cross section σtt=7.5±1.0 (stat+syst)  pb. The magnitude of the Cabibbo-Kobayashi-Maskawa matrix element, |Vtb|=0.97±0.05 (stat+syst) is extracted assuming three generations of quarks, and a lower limit of |Vtb|>0.89 at 95% credibility level is set.