An approximate theory is presented which involves the broadening of propagated Gaussian pulses in single-mode optical fibers by the first-oredr dispersion. The light source is assumed to have a Lorentz spectral distribution. Formulas are derived for the ensemble average of the pulse power and the rms pulse width. The approximate expressions are quite precise in comparison with the numerical calculations with deviations between the approximate expressions and the numerical calculations smaller than 5%.