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Sleep scheduling, which is putting some sensor nodes into sleep mode without harming network functionality, is a common method to reduce energy consumption in dense wireless sensor networks. This paper proposes a distributed and energy efficient sleep scheduling and routing scheme that can be used to extend the lifetime of a sensor network while maintaining a user defined coverage and connectivity. The scheme can activate and deactivate the three basic units of a sensor node (sensing, processing, and communication units) independently. The paper also provides a probabilistic method to estimate how much the sensing area of a node is covered by other active nodes in its neighborhood. The method is utilized by the proposed scheduling and routing scheme to reduce the control message overhead while deciding the next modes (full-active, semi-active, inactive/sleeping) of sensor nodes. We evaluated our estimation method and scheduling scheme via simulation experiments and compared our scheme also with another scheme. The results validate our probabilistic method for coverage estimation and show that our sleep scheduling and routing scheme can significantly increase the network lifetime while keeping the message complexity low and preserving both connectivity and coverage.