We report on the first measurement of the rapidity distribution, $d\sigma/dy$, over the full kinematic range for $e^+e^-$ pairs in the $Z$ boson region of $66116$~GeV$/c^2$. The data sample consists of 108~pb$^{-1}$ of $p\bar{p}$ collisions at $\sqrt{s}=1.8$~TeV taken by the Collider Detector at Fermilab during 1992--1995. The total cross section in the $Z$-boson region is measured to be $252 \pm 11$ pb. The total cross section and $d\sigma/dy$ are compared with Quantum Chromodynamics calculations in leading order, next-to-leading-order (NLO), next-to-next-leading-order, and NLO with gluon resummation. Posted to /cdf/pub/thesis/cdf5405_liu_thesis.ps http://www-cdf.fnal.gov/thesis/cdf5405_liu_thesis.ps Posted by liujb@cdfsga