  Atomic spin polarization of alkali atoms in the ground state can survive
thousands of collisions with paraffin-coated cell walls. The resulting long
spin-relaxation times achieved in evacuated, paraffin-coated cells enable
precise measurement of atomic spin precession and energy shifts of ground-state
Zeeman sublevels. In the present work, nonlinear magneto-optical rotation with
frequency-modulated light (FM NMOR) is used to measure magnetic-field-induced
spin precession for rubidium atoms contained in a paraffin-coated cell. The
magnetometric sensitivity of FM NMOR for the rubidium D2 line is studied as a
function of light power, detuning, frequency-modulation amplitude, and rubidium
vapor density. For a 5-cm diameter cell at temperature T ~ 35 degrees C, the
optimal shot-noise-projected magnetometric sensitivity is found to be 2 x
10^{-11} G/Hz^{1/2} (corresponding to a sensitivity to spin precession
frequency of ~ 10 microHz/Hz^{1/2} or a sensitivity to Zeeman sublevel shifts
of ~ 4 x 10^{-20} eV/Hz^{1/2}).
