Let's break down each scenario to determine whether it is a discrete random variable, continuous random variable, or not a random variable.

a. The amount of rain in City B during April

• Rainfall can take any value (e.g., 1.25 inches, 2.7 inches), and there are infinitely many possible values it can take within a given range. Therefore, it is a continuous random variable.
• Answer: A. It is a continuous random variable.

Now let’s look at the others for full clarity:

b. The square footage of a house

• The square footage of a house can also take any value, typically measured in decimals or fractions (e.g., 1200.5 square feet). Since it can take any value in a range, it is a continuous random variable.

c. The response to the survey question "Did you smoke in the last week?"

• The possible responses to this question are categorical ("Yes" or "No"), so it doesn't vary in a numerical sense like a random variable does. Therefore, this is not a random variable.

d. The amount of snowfall in December in City A

• Like rainfall, snowfall can take any value within a range, such as 5.3 inches, 12.7 inches, etc. This means it is a continuous random variable.

e. The number of free-throw attempts before the first shot is made

• The number of attempts before the first successful shot can only be a whole number (e.g., 1, 2, 3), making this a discrete random variable.

f. The number of hits to a website in a day

• The number of website hits is a countable value (e.g., 100, 500, 1000), so this is also a discrete random variable.

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Do you need more details or have any other questions?

Here are some relative questions for practice:

1. Is the time it takes to complete a task a discrete or continuous random variable?
2. What type of variable is the number of cars sold by a dealership in a week?
3. How would you classify the weight of newborn babies in a hospital?
4. Is the number of students in a classroom a discrete or continuous variable?
5. Would the temperature in a city over a year be a discrete or continuous random variable?

Tip: Discrete random variables are countable, while continuous random variables can take any value in a range.