A probabilistic framework is developed for quantifying the combined effect of uncertain parameters in sound insulation measurements, such as test sample dimensions, room properties, and loudspeaker positions, on the sound insulation values. The joint probability distribution of the uncertain parameters is constructed from the available information by means of a maximum entropy approach. The resulting sound insulation predictions are fully compatible with the available information but otherwise maximally conservative, so that the robustness of the predictions is guaranteed. Fundamental insight in the inherent uncertainty of the measurement procedure for airborne sound insulation is obtained by combining the method with detailed numerical simulations of the measurement procedure for single and double walls. The resulting uncertainty levels are very large, especially in the lowest frequency bands, and agree with experimental results. Furthermore, the probability distribution of the band-averaged sound reduction index of modally sparse walls can be of bimodal form.