Let's go through each of the scenarios and determine whether they represent a continuous random variable, discrete random variable, or are not random variables:

a. The amount of rain in City A during July

The amount of rain is measured in some continuous unit, like inches or millimeters, and it can take any value within a range. So, this would be:

• Answer: B. It is a continuous random variable.

b. The usual mode of transportation of people in City A

This refers to categories, such as "car," "bus," "bicycle," etc. These are not numerical values, but rather categorical. Since there is no random numerical value associated with this, it is not a random variable.

• Answer: C. It is not a random variable.

c. The height of a randomly selected person

Height is a continuous measure that can take on any value within a range (like centimeters or inches). Thus, it is a continuous random variable.

• Answer: B. It is a continuous random variable.

d. The time it takes for a light bulb to burn out

Time can take on any value within a range, measured in seconds, minutes, or hours. Therefore, this is a continuous random variable.

• Answer: B. It is a continuous random variable.

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

This counts the number of attempts, which is a discrete, whole number. The possible outcomes are countable (1, 2, 3,...). Thus, this is a discrete random variable.

• Answer: A. It is a discrete random variable.

f. The number of people with blood type B in a random sample of 38 people

This counts the number of people, which is also a discrete, whole number. The number of people with blood type B is countable, making this a discrete random variable.

• Answer: A. It is a discrete random variable.

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Summary of Answers:

• a. B. It is a continuous random variable.
• b. C. It is not a random variable.
• c. B. It is a continuous random variable.
• d. B. It is a continuous random variable.
• e. A. It is a discrete random variable.
• f. A. It is a discrete random variable.

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Do you want more details or have any questions?

Related Questions:

1. What distinguishes a discrete random variable from a continuous one?
2. Can categorical variables ever be treated as random variables?
3. What are examples of continuous random variables in real-world applications?
4. How do you calculate probabilities for discrete vs. continuous random variables?
5. What is the significance of a probability distribution for a random variable?

Tip: A continuous random variable has an infinite number of possible values within a range, while a discrete random variable has countable values.