Range prediction is a standard feature in most modern road vehicles, allowing drivers to make informed decisions about when to refuel. Most vehicles make range predictions through data- or model-driven means, monitoring the average fuel consumption rate or using a tuned vehicle model to predict fuel consumption. The uncertainty of future driving conditions makes the range prediction problem challenging, particularly for less pervasive battery electric vehicles (BEV). Most contemporary machine learning-based methods attempt to forecast the battery SOC discharge profile to predict vehicle range. In this work, we propose a novel approach using two recurrent neural networks (RNNs) to predict the remaining range of BEVs and the minimum charge required to safely complete a trip. Each RNN has two outputs that can be used for statistical analysis to account for uncertainties; the first loss function leads to mean and variance estimation (MVE), while the second results in bounded interval estimation (BIE). These outputs of the proposed RNNs are then used to predict the probability of a vehicle completing a given trip without charging, or if charging is needed, the remaining range and minimum charging required to finish the trip with high probability. Training data was generated using a low-order physics model to estimate vehicle energy consumption from historical drive cycle data collected from medium-duty last-mile delivery vehicles. The proposed method demonstrated high accuracy in the presence of day-to-day route variability, with the root-mean-square error (RMSE) below 6% for both RNN models.