Which of these represents a binomial question? A.) How many animals do you own? B.) How does being a pet owner make you feel? C.) Do you own a rabbit? D.) What are the names of your pets
The Correct Answer and Explanation is:
The correct answer is: C.) Do you own a rabbit?
Explanation
A binomial question is one that has only two possible outcomes. These outcomes are often described as “success” or “failure” or more simply as “yes or no”, true or false, or any two distinct categories. Binomial questions are essential in statistics, especially in the binomial distribution, which models the number of successes in a fixed number of independent trials with only two possible outcomes per trial.
Let us analyze each option to determine whether it qualifies as a binomial question:
- A.) How many animals do you own?
This is not a binomial question. It asks for a numerical value and can have a wide range of answers (0, 1, 2, 3, etc.). It is a quantitative question and not limited to just two possible outcomes. - B.) How does being a pet owner make you feel?
This is an open-ended question. It can generate a wide range of subjective responses such as happy, relaxed, stressed, or fulfilled. Since the number of potential answers is not limited to two, it is not binomial. - C.) Do you own a rabbit?
This is a binomial question because it has only two possible responses: yes or no. It fits the definition perfectly since it categorizes a single outcome into one of two possible groups. Such binary responses are key in binomial experiments. - D.) What are the names of your pets?
Like option B, this is an open-ended question. It allows for a wide variety of answers and is not restricted to two outcomes, so it is not binomial.
Therefore, option C is the only question that represents a binomial variable and can be used in binomial statistical analysis.
