Math Problem Statement

Determine whether the following value is a continuous random​ variable, discrete random​ variable, or not a random variable.

a. The square footage of a poolsquare footage of a pool

b. The hair color of adults in the United Stateshair color of adults in the United States

c. The number of statistics students now doing their homeworknumber of statistics students now doing their homework

d. The time it takes to drive from City Upper A to City Upper Btime it takes to drive from City A to City B

e. The time required to upload a file to the Internettime required to upload a file to the Internet

f. The height of a randomly selected personheight of a randomly selected person

Question content area bottom

Part 1

a. Is the

square footage of a poolsquare footage of a pool

a discrete random​ variable, continuous random​ variable, or not a random​ variable?

A.

It is a

discretediscrete

random variable.

B.

It is a

continuouscontinuous

random variable.

C.

It is not a random variable.

Part 2

b. Is the

hair color of adults in the United Stateshair color of adults in the United States

a discrete random​ variable, continuous random​ variable, or not a random​ variable?

A.

It is a discrete random variable.

B.

It is a continuous random variable.

C.

It is not a random variable.

Part 3

c. Is the

number of statistics students now doing their homeworknumber of statistics students now doing their homework

a discrete random​ variable, continuous random​ variable, or not a random​ variable?

A.

It is a

discretediscrete

random variable.

B.

It is a

continuouscontinuous

random variable.

C.

It is not a random variable.

Part 4

d. Is the

time it takes to drive from City Upper A to City Upper Btime it takes to drive from City A to City B

a discrete random​ variable, continuous random​ variable, or not a random​ variable?

A.

It is a

discretediscrete

random variable.

B.

It is a

continuouscontinuous

random variable.

C.

It is not a random variable.

Part 5

e. Is the

time required to upload a file to the Internettime required to upload a file to the Internet

a discrete random​ variable, continuous random​ variable, or not a random​ variable?

A.

It is a

continuouscontinuous

random variable.

B.

It is a

discretediscrete

random variable.

C.

It is not a random variable.

Part 6

f. Is the

height of a randomly selected personheight of a randomly selected person

a discrete random​ variable, continuous random​ variable, or not a random​ variable?

A.

It is a

continuouscontinuous

random variable.

B.

It is a

discretediscrete

random variable.

C.

It is not a random variable.

Solution

Let's analyze each of these cases individually.

Part 1

a. The square footage of a pool:

  • Explanation: Since square footage can take any value within a certain range, it is measurable and can vary continuously.
  • Answer: B. It is a continuous random variable.

Part 2

b. The hair color of adults in the United States:

  • Explanation: Hair color is categorical (e.g., black, brown, blonde), and thus not quantifiable on a numerical scale that would fit a discrete or continuous random variable framework.
  • Answer: C. It is not a random variable.

Part 3

c. The number of statistics students now doing their homework:

  • Explanation: The number of students is a countable quantity, which can take specific integer values (e.g., 0, 1, 2, …). This makes it a discrete random variable.
  • Answer: A. It is a discrete random variable.

Part 4

d. The time it takes to drive from City A to City B:

  • Explanation: Time can take any value within a range and can be measured to any level of precision (minutes, seconds, etc.), so it is a continuous variable.
  • Answer: B. It is a continuous random variable.

Part 5

e. The time required to upload a file to the Internet:

  • Explanation: Like the previous example, time can take any continuous value and be measured with increasing precision.
  • Answer: A. It is a continuous random variable.

Part 6

f. The height of a randomly selected person:

  • Explanation: Height is a continuous measurement, capable of taking any value within a range and measurable to any degree of precision.
  • Answer: A. It is a continuous random variable.

Recap of Answers:

  1. a. B. It is a continuous random variable.
  2. b. C. It is not a random variable.
  3. c. A. It is a discrete random variable.
  4. d. B. It is a continuous random variable.
  5. e. A. It is a continuous random variable.
  6. f. A. It is a continuous random variable.

Would you like further explanations on any of these answers or related examples?

Related Questions:

  1. What is the difference between continuous and discrete random variables in practical terms?
  2. How would we categorize variables like "age" or "temperature"?
  3. Can a categorical variable ever be considered a random variable?
  4. How do we approach random variables with mixed characteristics (e.g., time rounded to the nearest minute)?
  5. What role does precision play in distinguishing between continuous and discrete variables?

Tip:

A continuous random variable can theoretically take any value within a range, while a discrete random variable has distinct, countable outcomes.

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Random Variables
Discrete vs Continuous Variables

Formulas

-

Theorems

Classification of random variables (discrete and continuous)

Suitable Grade Level

Grades 10-12

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