This paper proposes a formulation for a stochastic security constrained unit commitment, dispatch and reserve scheduling, considering non-spinning reserves. We employ a randomized optimization technique that is based on scenario generation of the uncertain variables, in this case the wind power, and offers probabilistic certificates regarding the robustness properties of the resulting solution. To demonstrate the efficacy of the proposed methodology, we carry out a simulation based study on the IEEE 30 bus system comparing the proposed formulation to other variants, as well as examine its behavior on networks with different congestion levels. In all case studies, we verify empirically, via Monte Carlo simulations, the probabilistic performance of our solution methodology.