Forecasting distribution system loads is frequently fraught with uncertainties. Such uncertain-ties impose some undesirable consequences and fluctu-ations on the power working of the system leading to a decrease in the accuracy of the results obtained through system analysis. As a result, probabilistic analysis of the distribution system is extremely important. Hence, this paper presents a new probabilistic load flow approach in the presence of a 24-hour load shifting regime in all periods by applying a normal probability distribution in seven degrees of separation for the loads and employing this distribution function using Forward-backward algorithms based on Moth-Flame Optimization (MOF) aiming to identify the optimal placement and sizing of the Distributed Generation (DG). Our new proposed approach is tested on IEEE IO-bus and 33-bus radial distribution networks. The findings are compared with the conventional approach (i.e., based on deterministic techniques), and it is more efficient with minimum power cost for the user. © 2022 IEEE.