At the Fermilab Tevatron proton-antiproton ($pbar{p}$) collider, Drell-Yan lepton pairs are produced in the process $p bar{p} rightarrow e^+e^- + X$ through an intermediate $gamma^*/Z$ boson. The forward-backward asymmetry in the polar-angle distribution of the $e^-$ as a function of the $e^+e^-$-pair mass is used to obtain $sin^2theta^{rm lept}_{rm eff}$, the effective leptonic determination of the electroweak-mixing parameter $sin^2theta_W$. The measurement sample, recorded by the Collider Detector at Fermilab (CDF), corresponds to 9.4~fb$^{-1}$ of integrated luminosity from $pbar{p}$ collisions at a center-of-momentum energy of 1.96 TeV, and is the full CDF Run II data set. The value of $sin^2theta^{rm lept}_{rm eff}$ is found to be $0.23248 pm 0.00053$. The combination with the previous CDF measurement based on $mu^+mu^-$ pairs yields $sin^2theta^{rm lept}_{rm eff} = 0.23221 pm 0.00046$. This result, when interpreted within the specified context of the standard model assuming $sin^2 theta_W = 1 - M_W^2/M_Z^2$ and that the $W$- and $Z$-boson masses are on-shell, yields $sin^2theta_W = 0.22400 pm 0.00045$, or equivalently a $W$-boson mass of $80.328 pm 0.024 ;{rm GeV}/c^2$.
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