From the macroscopic viewpoint for describing the acceleration behaviour of drivers, a weighted probabilistic cellular automaton model (the WP model, for short) is proposed by introducing a kind of random acceleration probabilistic distribution function. The fundamental diagrams, the spatiotemporal pattes, are analysed in detail. It is shown that the presented model leads to the results consistent with the empirical data rather well, nonlinear flow-density relationship existing in lower density regions, and a new kind of traffic phenomenon called neo-synchronized flow. Furthermore, we give the criterion for distinguishing the high-speed and low-speed neo-synchronized flows and clarify the mechanism of this kind of traffic phenomenon. In addition, the result that the time evolution of distribution of headways is displayed as a normal distribution further validates the reasonability of the neo-synchronized flow. These findings suggest that the diversity and the randomicity of drivers and vehicles have indeed a remarkable effect on traffic dynamics.