Questions: Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The time required to upload a file to the Internet b. The hair color of adults in the United States c. The time it takes for a light bulb to burn out d. The number of people in a restaurant that has a capacity of 150 e. The time it takes to drive from City A to City B f. The number of light bulbs that burn out in the next year in a room with 19 bulbs e. Is the time 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 discrete random variable. B. It is a continuous random variable. C. It is not a random variable.

Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The time required to upload a file to the Internet b. The hair color of adults in the United States c. The time it takes for a light bulb to burn out d. The number of people in a restaurant that has a capacity of 150 e. The time it takes to drive from City A to City B f. The number of light bulbs that burn out in the next year in a room with 19 bulbs e. Is the time 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 discrete random variable. B. It is a continuous random variable. C. It is not a random variable.
Transcript text: Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The time required to upload a file to the Internet b. The hair color of adults in the United States c. The time it takes for a light bulb to burn out d. The number of people in a restaurant that has a capacity of 150 e. The time it takes to drive from City A to City B f. The number of light bulbs that burn out in the next year in a room with 19 bulbs e. Is the time 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 discrete random variable. B. It is a continuous random variable. C. It is not a random variable.
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Solution

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Solution Steps

To determine whether a value is a continuous random variable, discrete random variable, or not a random variable, consider the nature of the data:

  • A continuous random variable can take any value within a given range (e.g., time, weight).
  • A discrete random variable can take specific, separate values (e.g., number of people, number of items).
  • If the value is not numerical or does not vary, it is not a random variable.

For the first three parts: a. The time required to upload a file to the Internet is a continuous random variable because time can take any value within a range. b. The hair color of adults in the United States is not a random variable because it is categorical, not numerical. c. The time it takes for a light bulb to burn out is a continuous random variable because time can take any value within a range.

Step 1: Classify the First Variable

The first variable is "The time required to upload a file to the Internet." Since time can take any value within a range, it is classified as a continuous random variable. Thus, we have: \[ \text{Classification: Continuous random variable} \]

Step 2: Classify the Second Variable

The second variable is "The hair color of adults in the United States." This variable is categorical and does not represent numerical values that can vary. Therefore, it is classified as not a random variable: \[ \text{Classification: Not a random variable} \]

Step 3: Classify the Third Variable

The third variable is "The time it takes for a light bulb to burn out." Similar to the first variable, this is also a measure of time, which can take any value within a range. Hence, it is classified as a continuous random variable: \[ \text{Classification: Continuous random variable} \]

Final Answer

The classifications for the variables are as follows:

  1. The time required to upload a file to the Internet: \(\text{Continuous random variable}\)
  2. The hair color of adults in the United States: \(\text{Not a random variable}\)
  3. The time it takes for a light bulb to burn out: \(\text{Continuous random variable}\)

Thus, the final answer is: \[ \boxed{ \begin{align*}

  1. & \text{ Continuous random variable} \\
  2. & \text{ Not a random variable} \\
  3. & \text{ Continuous random variable} \end{align*} } \]
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