Machine-type-communications have attracted a lot of interest in the past years. They rely on interactions between devices with no human supervision. This will help to the advent of a plethora of applications such as the Internet-of-Things. Part of the research within this field deals with coordinating the access of a large number of devices to the network, the so-called \textit{massive} machine-type-communications. In this paper, we focus on the evaluation of the data rate for that scenario, based on an approximation of the statistics of the aggregated interference that depends on the sensors activity. We will consider that the sensors can be in either active or sleep mode, modeled as a Bernoulli random variable. This results in an aggregated interference that follows a discrete distribution whose computation becomes unfeasible with the number of devices. That is why two alternatives are presented to replace the original magnitude and work with an analytic closed form expression approximating the actual statistics. Our approaches are derived using the Chernoff bound and a Gaussian approximation based on Lyapunov's central limit theorem. The average rate is found in both cases and compared with the actual values in different setups. Monte-Carlo simulations will be used for this task.