Final answer:
The correct option for a discrete random variable from the given choices is 'e) The number of beverages sold at a lemonade stand.' It exemplifies countable outcomes, distinguishing it from continuous variables that involve measurement and can take on any value within an interval.
Step-by-step explanation:
Understanding the difference between discrete random variables and continuous random variables is important in statistics. A discrete random variable can take on countable values, typically whole numbers, as a result of a random process. The question asks for an example of a discrete random variable, and the correct option from those provided is 'e) The number of beverages sold at a lemonade stand.'
This is a discrete random variable because you can count the number of beverages as whole units; it is not possible to sell a fraction of a beverage. Other options like the time to finish a marathon or the temperature of a pot roast involve measurements and are hence continuous random variables.
In contrast, continuous random variables can take on any value within an interval and are measured rather than counted. The temperature, time, and rainfall mentioned in other options of the question fall under this category.
To summarize, both types of variables play a crucial role in statistical analysis and are applied to different situations depending on whether the outcome of an experiment is countable or measurable.