Simulation modeling plays a significant role in many real-world applications. Let's consider a scenario where a manufacturing company aims to optimize production planning by simulating the uncertain demand for its products. In this case, a simulation model with a discrete probability distribution can be utilized. How would you construct and interpret a simulation model that implements a discrete probability distribution to represent the uncertain demand? What considerations would you take into account when selecting the appropriate discrete probability distribution? Can you provide real-world examples where discrete probability distributions are commonly used to model uncertain quantities?