Distribution of Δ from the fitted GRB spectra (top). Uncertainty on Δ is included via the marginal posteriors of each fit. Lower panel: marginal distributions of Δ for simulated synchrotron spectra with p = 2, 4. The 68% credible regions for these fits are superimposed on the full distribution. This demonstrates that the theoretical widths from pure synchrotron emission are consistent with the widths derived from the sample.