Final answer:
The variable n is a binomial variable as it meets the criteria of fixed number of independent trials, two possible outcomes, and a constant probability of success.
Step-by-step explanation:
The variable n, which represents the number of orders containing at least one pair of men's athletic shoes that Lionel rings up, is a binomial variable. This is because there are a fixed number of trials (8 orders), each trial is independent (each order is independent of the others), the outcome of each trial falls into one of two categories (either at least one pair of men's athletic shoes is included or not), and the probability of success (an order containing at least one pair of men's athletic shoes) is constant (20%). Therefore, the type of variable is A. Binomial.