Question

Is this variable discrete or continuous? Why?

The number of people in the stadium at a UCF football game.
A. Discrete because there are an uncountable number of possible outcomes
B. Continuous because there are a countable number of possible outcomes that can be listed
C. Discrete because there are a countable number of possible outcomes that can be listed
D. Discrete because there are an uncountable number of possible outcomes
E. Neither discrete nor continuous

Answer 1

The number of people in a stadium is a discrete variable because it represents a countable number of individuals that can be listed.

Therefore, the correct answer is: option C). Discrete because there are a countable number of possible outcomes that can be listed.

Step-by-step explanation:

The number of people in the stadium at a UCF football game would be a discrete random variable. This is because the number of people can be counted and there are a finite number of seats in the stadium, making the possible outcomes countable.

Furthermore, it does not make sense to have a non-integer number of people, so the variable cannot be continuous. Discrete random variables have countable outcomes, such as the number of heads when flipping a coin or the number of red balls in a container.

On the other hand, continuous random variables are measured and have uncountable outcomes, like the height of a person or the temperature of a day.

Based on these definitions, the correct answer to the student's question is: C. Discrete because there are a countable number of possible outcomes that can be listed.