A whole body counter (WBC) designed to measure bremsstrahlung from 90Y, the short-lived daughter of 90Sr, has been used since 1974 to measure 90Sr-body burdens in residents along the Techa River, which was contaminated by releases from the Mayak Production Association. Bayes' rule has been applied to the a posteriori WBC data in order to derive the uncertainties associated with the data: The lower limit of reliable detection is 2.0 kBq and the uncertainty of routine measurements is 1.6 kBq.