Final answer:
The variable n is a discrete random variable representing the countable number of orders containing men's athletic shoes that Lionel rings up.
Step-by-step explanation:
The student asked about the type of variable that n represents in the context where 'n' is the number of orders Lionel rings up that include at least one pair of men's athletic shoes, given that 20% of the pairs of shoes sold are men's athletic shoes.
The variable n can be classified as a discrete random variable because it represents a countable number of outcomes where each outcome is the number of orders containing men's athletic shoes.