Let's analyze each part based on the given descriptions:

Part 1

a. Responses to the survey question "How many pets do you have?"

• Since the outcomes are countable (number of pets can be 0, 1, 2, etc.), this is a discrete random variable.

Part 2

b. Responses to the survey question "Do you have health insurance?"

• Since the outcomes are not numerical (responses are typically "Yes" or "No"), this is not a random variable.

Part 3

c. Number of families that must be surveyed before finding one with 10 pets

• Since the outcomes are countable (1 family, 2 families, etc., until finding one with 10 pets), this is a discrete random variable.

Part 4

d. Exact weights of the next 500 puppies born in a region

• Since the outcomes are not countable (weight is a continuous measurement and can take any value within a range), this is a continuous random variable.

Part 5

e. Exact head circumference of human males

• Since the outcomes are not countable (head circumference is a continuous measurement and can take any value within a range), this is a continuous random variable.

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Summary of Responses:

1. a: Discrete random variable.
2. b: Not a random variable.
3. c: Discrete random variable.
4. d: Continuous random variable.
5. e: Continuous random variable.

Would you like further explanations on any part of this answer?

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Additional Related Questions

1. What is the difference between discrete and continuous random variables?
2. Why is "Yes" or "No" not considered a numerical outcome?
3. Can a variable be both discrete and continuous? If so, in what context?
4. How are random variables used in probability and statistics?
5. How do we determine if a random variable is countable or not?

Tip

When determining the type of random variable, ask whether the possible values can be counted (discrete) or if they span a range of values without gaps (continuous).