Timing uncertainties which originate in the electron transit time spread in a photomultiplier tube are calculated under the assumption that errors vary inversely with the square root of the number of photoelectrons produced by a scintillation. Delayed coincidence line shapes are calculated for a uniform pulse height distribution and for the pulse height distribution which results from elastic scattering of monoenergetic neutrons in an organic scintillator. No detection threshold is imposed but in each case the analysis may be easily modified to incorporate one. The line shapes which result are not markedly wider than the gaussian distribution which would result from accepting only spectrum cutoff size pulses for timing. The line shapes are also independent of spectrum cutoff and scale with this gaussian distribution. Several characteristic properties of these resolution functions are discussed.