  The probability distribution of lens image separations is calculated for the
``standard'' gravitational lensing statistics model in an arbitrary, flat
Robertson-Walker universe, where lensing galaxies are singular isothermal
spheres that follow the Schechter luminosity function. In a flat universe, the
probability distribution is independent of the source distribution in space and
in brightness. The distribution is compared with observed multiple-image lens
cases through Monte-Carlo simulations and the Kolmogorov-Smirnov test. The
predicted distribution depends on the shape of the angular selection bias used,
which varies for different observations. The test result also depends on which
lens systems are included in the samples. We mainly include the lens systems
where a single galaxy is responsible for lensing. We find that the ``standard''
model predicts a distribution which is different from the observed one.
However, the statistical significance of the discrepancy is not large enough to
invalidate the ``standard'' model with high confidence. Only the radio data
reject the model at the 95% confidence level, which is based on four/three lens
cases. Therefore, we cannot say that the observational data reject the
``standard'' model with enough statistical confidence. However, if we take the
velocity dispersion of dark matter without the conversion factor (3/2)^(1/2)
from that of luminous matter, the discrepancy is quite severe, and even the
ground-based optical survey data reject the ``standard'' model with > ~90%
confidence.
