  We use very precise frequencies of low-degree solar-oscillation modes
measured from 4752 days of data collected by the Birmingham Solar-Oscillations
Network (BiSON) to derive seismic information on the solar core. We compare
these observations to results from a large Monte Carlo simulation of standard
solar models, and use the results to constrain the mean molecular weight of the
solar core, and the metallicity of the solar convection zone. We find that only
a high value of solar metallicity is consistent with the seismic observations.
We can determine the mean molecular weight of the solar core to a very high
precision, and, dependent on the sequence of Monte Carlo models used, find that
the average mean molecular weight in the inner 20% by radius of the Sun ranges
from 0.7209 to 0.7231, with uncertainties of less than 0.5% on each value. Our
lowest seismic estimate of solar metallicity is Z=0.0187 and our highest is
Z=0.0239, with uncertainties in the range of 12--19%. Our results indicate that
the discrepancies between solar models constructed with low metallicity and the
helioseismic observations extend to the solar core and thus cannot be
attributed to deficiencies in the modeling of the solar convection zone.
