Let's analyze and solve the given problem step by step.

Problem Analysis:

You need to determine whether the random variable in each case is discrete or continuous, and justify the reasoning.

1. (a) A person’s height

   • Nature: Continuous.
     Height can take any value within a range (e.g., 165.2 cm, 165.25 cm, etc.), so it is measured on a continuous scale.

2. (b) A student’s course grade

   • Nature: Discrete.
     Course grades (e.g., A, B, C, D, F) are categorical and have specific possible outcomes, making them discrete.

3. (c) The thickness of a metal plate

   • Nature: Continuous.
     Thickness can take any value within a range, even to many decimal places (e.g., 1.02 mm, 1.025 mm).

4. (d) The purity of a chemical solution

   • Nature: Continuous.
     Purity is often measured as a percentage or a fraction (e.g., 99.97%), which can vary continuously.

5. (e) The type of personal computer a person owns

   • Nature: Discrete.
     The type of computer is categorical, with a fixed number of options (e.g., laptop, desktop, tablet).

6. (f) A person’s age

   • Nature: Continuous.
     While we often measure age in whole numbers (e.g., 25 years), it is inherently continuous (e.g., 25.5 years).

Final Answer Summary:

Would you like me to expand on any of the reasoning?

Related Questions:

1. What are the key differences between discrete and continuous random variables?
2. Can you give real-world examples of discrete and continuous variables?
3. How do we represent continuous random variables mathematically (e.g., probability density functions)?
4. Why is "type of personal computer" considered a discrete variable even though there may be many types?
5. How can age, typically measured in whole numbers, still be classified as continuous?

Tip:

For continuous random variables, think about measurements that could theoretically be infinitely precise, whereas discrete variables represent countable or categorized data.