  The electron energy distribution index, p, is a fundamental parameter of the
synchrotron emission from a range of astronomical sources. Here we examine one
such source of synchrotron emission, Gamma-Ray Burst afterglows observed by the
Swift satellite. Within the framework of the blast wave model, we examine the
constraints placed on the distribution of p by the observed X-ray spectral
indices and parametrise the distribution. We find that the observed
distribution of spectral indices are inconsistent with an underlying
distribution of p composed of a single discrete value but consistent with a
Gaussian distribution centred at p = 2.36 and having a width of 0.59.
Furthermore, accepting that the underlying distribution is a Gaussian, we find
the majority (>94%) of GRB afterglows in our sample have cooling break
frequencies less than the X-ray frequency.
