Traffic dynamics on freeways are stochastic in nature because of errors in perception and operation of drivers as well as the heterogeneity between and within drivers. This stochasticity is often represented in car-following models by a stochastic term, which is assumed to follow a normal distribution for the convenience of mathematical processing. However, the validity of this assumption has not been studied yet. In this study, we focused on the shape of the distribution of a stochastic term in the car-following model that predicts an acceleration after a time step. Based on vehicle trajectory data on a freeway in Japan, a car-following model is first developed by using data-driven methodology in which long short-term memory (LSTM) network is applied. In this LSTM network, the acceleration value is discretized and the model parameters are trained with the focal loss function. The relationship between the predicted distributions’ modality, standard deviation (SD), and (Formula presented.) with respect to traffic states is then examined. The findings demonstrate that: 1) the developed model can accurately predict the accelerations; 2) a probabilistic distribution tends to have a large SD and multimodality around a merging point and at the beginning of and along stop-and-go waves; and 3) driving behavior can be classed in one of four clusters based on the variation of the percentile value that a driver takes within the probability distribution. The proposed model and the insights are helpful for improving microscopic simulation models when considering new traffic management measures.