Resource allocation for cloud services is a complex task due to the diversity of the services and the dynamic workloads. One way to address this is by overprovisioning which results in high cost due to the unutilized resources. A much more economical approach, relying on the stochastic nature of the demand, is to allocate just the right amount of resources and use additional more expensive mechanisms in case of overflow situations where demand exceeds the capacity. In this paper we study this approach and show both by comprehensive analysis for independent normal distributed demands and simulation on synthetic data that it is significantly better than currently deployed methods.