Network slicing allows Mobile Network Operators to split the physical infrastructure into isolated virtual networks (slices), managed by Service Providers to accommodate customized services. The Service Function Chains (SFCs) belonging to a slice are usually deployed on a best-effort premise: nothing guarantees that network infrastructure resources will be sufficient to support a varying number of users, each with uncertain requirements. Taking the perspective of a network Infrastructure Provider (InP), this paper proposes a resource provisioning approach for slices, robust to a partly unknown number of users with random usage of the slice resources. The provisioning scheme aims to maximize the total earnings of the InP, while providing a probabilistic guarantee that the amount of provisioned network resources will meet the slice requirements. Moreover, the proposed provisioning approach is performed so as to limit its impact on low-priority background services, which may co-exist with slices in the infrastructure network. Taking all these constraints into account leads to an integer programming problem with many nonlinear constraints. These constraints are first relaxed to get an integer linear programming formulation of the slice resource provisioning problem. This problem is then solved considering the slice resource provisioning demands jointly. A suboptimal approach is finally proposed where slice resource provisioning demands are considered sequentially. Both solutions are compared to provisioning schemes that do not account for best-effort services sharing the common infrastructure network, as well as uncertainties in the slice resource demands.