The Internet of Things (IoT) promises a revolution in the monitoring and control of a wide range of applications, from urban water supply networks and precision agriculture food production, to vehicle connectivity and healthcare monitoring. For applications in such critical areas, control software and protocols for IoT systems must be verified to be both robust and reliable. Two of the largest obstacles to robustness and reliability in IoT systems are effects on the hardware caused by environmental conditions, and the choice of parameters used by the protocol. In this paper we use probabilistic model checking to verify that a synchronisation and dissemination protocol for Wireless Sensor Networks (WSNs) is correct with respect to its requirements, and is not adversely affected by the environment. We show how the protocol can be converted into a logical model and then analysed using the probabilistic model-checker, PRISM. Using this approach we prove under which circumstances the protocol is guaranteed to synchronise all nodes and disseminate new information to all nodes. We also examine the bounds on synchronisation as the environment changes the performance of the hardware clock, and investigate the scalability constraints of this approach.