We suggest a new method for constructing an ecient point predictor for the future order statistics when the sample size is a random variable. The suggested point predictor is based on some characterization properties of the distributions of order statistics. For several distributions, including the mixture distribution, the performance of the suggested predictor is evaluated by means of a comprehensive simulation study. Three examples of real lifetime data-sets are analyzed by using this method and compared with an ecient recent method given by Barakat et al. [1], that deals with non-random sample sizes. One of these examples predicts the accumulative new cases per million for infection of the new Coronavirus (COVID-19).