Due to the failure of deterministic point forecasting to capture the uncertainty associated with the original time series, and because it can reflect the range of electrical load fluctuation, the importance of probabilistic interval forecasting has gradually increased. However, the existing theoretical system of interval forecasting is still incomplete, is a complicated process, and has relatively low accuracy. The objective of this study is to propose an interval forecasting approach based on feature selection, the optimized machine learning method, and correction of the Gaussian distribution. By applying this approach, the distribution of predictions can be established to include all the information of prediction intervals at each confidence level, making the best use of the known information. The electrical load time series of Australia are used to examine the effectiveness of the proposed approach, and compared with other models, it is proven to not only simplify the forecasting process and shorten the processing time, but also significantly improve the forecasting efficiency, flexibility, and accuracy.