  We consider the effect of inhomogeneous neutrino degeneracy on Big Bang
nucleosynthesis for the case where the distribution of neutrino chemical
potentials is given by a Gaussian. The chemical potential fluctuations are
taken to be isocurvature, so that only inhomogeneities in the electron chemical
potential are relevant. Then the final element abundances are a function only
of the baryon-photon ratio $\eta$, the effective number of additional neutrinos
$\Delta N_\nu$, the mean electron neutrino degeneracy parameter $\bar \xi$, and
the rms fluctuation of the degeneracy parameter, $\sigma_\xi$. We find that for
fixed $\eta$, $\Delta N_\nu$, and $\bar \xi$, the abundances of helium-4,
deuterium, and lithium-7 are, in general, increasing functions of $\sigma_\xi$.
Hence, the effect of adding a Gaussian distribution for the electron neutrino
degeneracy parameter is to decrease the allowed range for $\eta$. We show that
this result can be generalized to a wide variety of distributions for $\xi$.
