This work studies the job sequencing and tool switching problem on non-identical parallel machines with stochastic processing times. We propose a single-stage stochastic MILP based on an improved position-based formulation that reduces the number of timing variables and simplifies the propagation of completion times along machine sequences. Processing time uncertainty is modeled using a scenario-based approach, where each scenario is associated with different processing times drawn from Normal distributions. Uncertainty is introduced into the model through scenario-dependent constraints, and the objective is to minimize the expected makespan over all scenarios. Computational results on benchmark instances show that the proposed model achieves solution quality comparable to or better than existing data-driven approaches, while significantly reducing computational effort, especially for medium and large instances.