Example: Given and find the probability that the value of in a new experiment is (1) between 4.5 and 5.5, (2) between 4.5 and 5.75, (3) less than 6.5 and (4) between 6 and 7.

Let and be the limits between which the probability must be determined. The values of in each case are (1) and 0.5, (2) and 0.75, (3) and (4) between 1 and 2. The required probabilities are ; hence in (1), this quantity is ; in (2), ; in (3), and in (4), .

The most commonly used probability interval called the confidence interval corresponds to since . Hence normally distributed scatter can be specified as with confidence. For convenience this interval is written as . Gaussian distribution for scatter can be assumed if the number of repetitive experiments is greater than 30.

For points with a mean , points that fall outside a probability value of are to be rejected. The mean and the variance and must then be recalculated. This is called Chauvenet's criterion for statistical rejection of data. The criterion can be applied only once to the data set. It determines the acceptable level of scatter in an experiment arising from a large number of random influences.