A large fraction of gamma-ray burst (GRB) spectra are very hard below the peak which indicates that the emission comes from the photosphere. The size of this fraction is investigated in two different ways. First, we use the theoretical spectrum expected from a non-dissipative flow to make synthetic Fermi/GBM spectra which are then fitted by the cut off power law function to simulate real data analysis. These results are compared these with observations made by the Fermi/GBM. We find that more than a quarter of the bursts in the GBM catalogue have at least one time-resolved spectrum, which is consistent with a non-dissipative flow. Second, we reanalyse a sample of peak spectra from strong bursts observed by Fermi. In particular we perform a model comparison between a non-dissipative photospheric model and a slow cooled synchrotron model based on Bayesian evidences. We find that the photospheric spectral shape is preferred by a majority of the spectra. This allows us to draw the conclusion that GRB spectra are indeed very narrow. The fraction of spectra consistent with emission from the photosphere will increase even more if dissipation of kinetic energy in the flow occurs below the photosphere. We discuss these findings in context of alternative emission models such as synchrotron emission from optically-thin shock regions.