Ground-based sub-mm (SCUBA) and mm-wavelength (MAMBO) blank-field surveys have identified more than 100 sources, the majority of which are believed to be dusty optically-obscured starburst galaxies. Colours derived from various combinations of FIR, submillimetre, millimetre, and radio fluxes provide the only currently available means to determine the redshift distribution of this new galaxy population. In this paper we apply a Monte-Carlo photometric-redshift technique to the multi-wavelength data available for 50 galaxies selected at 850 μm in wide-area SCUBA surveys. We calculate a probability distribution for the redshift of each galaxy, which includes a detailed treatment of the observational errors and uncertainties in the priors. The cumulative redshift distribution for this population is asymmetric, and broader than those published elsewhere, with a significant high-z tail. Approximately 40 to 90% of the sub-mm population is expected to have redshifts in the interval 2 ≤ z ≤ 4. We also show, however, that the colours of many (50%) individual sub-mm sources are consistent with those of starburst galaxies that lie at extreme redshifts, z > 4.
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