  A recent theory has provided a possible explanation for the ``non-universal
scaling'' of the low-temperature conductance (and conductivity) peak-heights of
two-dimensional electron systems in the integer and fractional quantum Hall
regimes. This explanation is based on the hypothesis that samples which show
this behavior contain density inhomogeneities. Theory then relates the
non-universal conductance peak-heights to the ``number of alternating
percolation clusters'' of a continuum percolation model defined on the
spatially-varying local carrier density. We discuss the statistical properties
of the number of alternating percolation clusters for Corbino disc samples
characterized by random density fluctuations which have a correlation length
small compared to the sample size. This allows a determination of the
statistical properties of the low-temperature conductance peak-heights of such
samples. We focus on a range of filling fraction at the center of the plateau
transition for which the percolation model may be considered to be critical. We
appeal to conformal invariance of critical percolation and argue that the
properties of interest are directly related to the corresponding quantities
calculated numerically for bond-percolation on a cylinder. Our results allow a
lower bound to be placed on the non-universal conductance peak-heights, and we
compare these results with recent experimental measurements.
