In this paper the problem of the most appropriate modeling of scarce information for an engineering analysis is investigated. This investigation is focused on a comparison between a rough probabilistic modeling based on the first two moments and interval modeling. In many practical cases, the available information is limited to such an extent that a more thorough modeling cannot be pursued. The engineer has to make a decision regarding the modeling of this limited and coarse information so that the results of the analysis provide the most suitable basis for conclusions. We approach this problem from the angle of information theory and propose to select the most informative model (in Shannon's sense). The investigation reveals that the answer to question of model choice depends on the confidence, which is needed for the engineering results in order to make informed decisions.