With most of the current probabilistic safety criteria (PSCs), it is difficult to select a unanimously acceptable single-point safety goal and to evaluate the uncertainties in the results of a probabilistic safety assessment (PSA). A new PSC is proposed, in which the distribution of the public’s safety goals (DPSG) is used as a benchmark for evaluating the results of a PSA rather than a single-point safety goal. With this approach, the DPSG and the uncertainties in the results of a PSA can be handled properly so as to give a clear answer of “how much of the public feels a nuclear reactor is safe” to the question of “How safe is safe enough?” The proposed PSC is compared with the current PSCs and the expected utility model. If the actual DPSG is unavailable or difficult to obtain directly, a lognormal distribution is recommended as an appropriate DPSG for core melt frequencies in terms of maximizing entropy and minimizing total social cost. The proposed DPSG and PSC for core melt frequency are applied to the results of NUREG-1150.