Uncertainty quantification has been recognized by the community as an essential component of best-estimate reactor analysis simulation because it provides a measure by which the credibility of the simulation can be assessed. In a companion manuscript, a framework for the propagation of nuclear data uncertainties from the multi-group level through lattice physics and core calculations and ultimately to core responses of interest, has been developed. The overarching goal of this framework is to automate the propagation, prioritization, mapping, and reduction of uncertainties for reactor analysis core simulation. This manuscript employs both heavy and light water reactor systems to exemplify the application of this framework. Specifically, the manuscript is limited to the propagation of the nuclear data starting with the multi-group cross-section covariance matrix and down to core responses, e.g., eigenvalue and power distribution, in steady state core wide calculations. The goal is to demonstrate how the framework employ reduction techniques to compress the uncertainty space into a very small number of active DOFs which renders the overall process computationally feasible for day-to-day engineering evaluations.