  We derive kinematic distances to the 86 6.7 GHz methanol masers discovered in
the Arecibo Methanol Maser Galactic Plane Survey. The systemic velocities of
the sources were derived from 13CO (J=2-1), CS (J=5-4), and NH3 observations
made with the ARO Submillimeter Telescope, the APEX telescope, and the
Effelsberg 100 m telescope, respectively. Kinematic distance ambiguities were
resolved using HI self-absorption with HI data from the VLA Galactic Plane
Survey. We observe roughly three times as many sources at the far distance
compared to the near distance. The vertical distribution of the sources has a
scale height of ~ 30 pc, and is much lower than that of the Galactic thin disk.
We use the distances derived in this work to determine the luminosity function
of 6.7 GHz maser emission. The luminosity function has a peak at approximately
10^{-6} L_sun. Assuming that this luminosity function applies, the methanol
maser population in the Large Magellanic Cloud and M33 is at least 4 and 14
times smaller, respectively, than in our Galaxy.
