  The NuTeV collaboration reported anomalously large weak mixing angle sin^2
theta_W in comparison with the standard model prediction. Neutrino and
antineutrino charged- and neutral-current events are analyzed for extracting
sin^2 theta_W. Although the Paschos-Wolfenstein relation is not directly used
in the analysis, it plays an important role in the determination. Noting that
the target nucleus, iron, is not an isoscalar nucleus, we derive a
leading-order expression for a modified Paschos-Wolfenstein relation for
nuclei, which may have neutron excess. Then, using charge and baryon-number
conservations for nuclei, we discuss a nuclear correction in the sin^2 theta_W
determination. It is noteworthy that nuclear modifications are different
between valence up- and down-quark distributions. We show this difference
effect on the NuTeV sin^2 theta_W deviation.
