The paper describes computing the information interval of an interval measurements sample of physical value (constant) under the interval bound of the measuring errors. The standard procedures of Interval Analysis are used. On the hypothesis of some density probabilities distribution law (DPDL) of the measuring errors (in the given bounds), the Monte-Carlo Method is applied to compute: the DPDL of the central point of the information interval and one of its radius. The most practically popular cases of the measuring error are considered: the uniform DPDL and the truncated Gaussian DPDL in the given interval. The investigation is stipulated by the experimentalists’ demands for building the mentioned DPDL of the output central point and radius. It is in contrast to the Interval Analysis standard on the hypothesis of complete absence of probabilistic information on the error. Simulation results (the histograms of the output estimates) are given.