Let's analyze the given options and determine whether each one refers to a discrete random variable, a continuous random variable, or if it is not a random variable.

Here’s how we can categorize them:

a. Exact weights of the next 200 puppies born in a region

• Weights are measured on a continuous scale (like 2.35 kg, 3.76 kg, etc.), and they can take any real value within a range. Hence, the outcomes are continuous.
• Answer: continuous random variable

b. Shoe sizes (such as 8 or 8 ½) of humans

• Shoe sizes are measured in discrete intervals (whole numbers or fractions like 8, 8 ½). The outcomes are a specific, countable set of values.
• Answer: discrete random variable

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

• The number of families is a count of discrete units (1 family, 2 families, etc.). This is a discrete countable value.
• Answer: discrete random variable

d. Responses to the survey question: “What is your natural hair color?”

• Hair color is categorical and non-numerical, so it doesn’t fit as a random variable.
• Answer: not a random variable

e. Exact hand span of human males

• Hand span is measured continuously (like 20.4 cm, 21.7 cm, etc.), meaning the outcomes are continuous.
• Answer: continuous random variable

Here is how the answers will look in the blank spaces:

1. a: continuous random variable
2. b: discrete random variable
3. c: discrete random variable
4. d: not a random variable
5. e: continuous random variable

Would you like further clarification or details on this? Here are five related questions to think about:

1. What is the main difference between discrete and continuous random variables?
2. Can categorical data ever be treated as a random variable? Why or why not?
3. How do we calculate probabilities for continuous random variables compared to discrete ones?
4. What are some common examples of continuous random variables in daily life?
5. In what scenarios would you encounter a variable that is not random at all?

Tip: A discrete random variable has a countable number of possible outcomes, while a continuous random variable has an uncountable number of possible outcomes, often corresponding to measurements.