A common practice in random noise measurements is to assume that the noise samples are normally distributed. Since the sound pressure level (Lp) is related with the sound energy by a non linear equation, the distribution of the two variables will be different. If one assumes that the probability density function (pdf) of Lp is normal, the pdf of noise energy is not and vice versa. A simple criterion based on statistical properties of sampled noise can be used for the determination of the kind of distribution of the measured noise. The case in which the noise energy emitted by the source, and the case in which the measured noise level is normally distributed are examined. For each case confidence intervals of the calculated equivalent level are calculated.