Wireless sensor networks (WSNs) have been the focus of many and high-relevant works. Nowadays, because of time-critical tasks of several applications, one of the new challenges faced in WSNs is to handle real-time data storage and query. Since in such networks energy is the crucial resource, it is challenging to design a query processing mechanism that meets both time constraints and energy. This paper addresses this challenge and proposes a new architecture that combines statistical modeling techniques with the distributed approach and a query processing algorithm to optimize the real-time user query processing. Such statistical model provides good approximate answers to queries with a given probabilistic confidence. This combination allows performing a query processing algorithm based on admission control that uses the error tolerance and the probabilistic confidence interval as admission parameters. The experiments based on real world as well as synthetic data sets demonstrate that the proposed solution optimizes the real-time query processing to save more energy while meeting time constraints.