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One scenario in which it might be more appropriate to model temperature using a discrete random variable is when tracking the temperature of a manufacturing process where the readings are taken at fixed intervals and the temperature range is divided into a few categories. For example, suppose there is a manufacturing process that is monitored every hour, and the temperature is essential for quality control. The operator could categorize the temperature readings into a few discrete categories: too cold, acceptable, and too hot. Each category could be assigned a numerical value, such as 0 for too cold, 1 for acceptable, and 2 for too hot. The reason this scenario benefits from using a discrete random variable rather than a continuous one is twofold: 1. Taking readings at fixed intervals naturally gives rise to discrete values since the temperature is measured at specific points in time, rather than throughout a continuous period. 2. By using a discrete random variable, the complexity of dealing with continuous data can be avoided, and the operator can focus on whether the temperature readings are within the acceptable range or not. This makes it more straightforward to make decisions related to quality control and adjusting the manufacturing process accordingly.