= Solution
A thermally populated extra light <neutrino> species is relativistic during nucleosynthesis; its $0.001\,{\rm eV}$ mass is negligible at MeV temperatures. One neutrino-antineutrino species adds $(7/8)\times2=7/4$ to $g_*$. Thus the expansion rate increases by $\sqrt{12.5/10.75}$ and the freeze-out temperature by $(12.5/10.75)^{1/6}$. Earlier freeze-out leaves more neutrons, while faster cooling leaves less time for decay. \b[The helium-4 abundance increases.] This assumes the new species was populated at the standard neutrino temperature; an unpopulated species would not contribute this extra density.
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