Identify the given item as probability distribution, continuous random variable, or discrete random variable.
The amount of time that an individual watches television.
a. discrete random variable
b. probability distribution
c. continuous random variable****
c. continuous random variable
The given item, "the amount of time that an individual watches television," can be identified as a continuous random variable.
To understand why this is the case, we need to define the different types of random variables:
1. Discrete random variable: A random variable that can take on a countable number of distinct values. For example, the number of children in a family or the number of cars in a parking lot are discrete random variables because they can only take on whole numbers.
2. Continuous random variable: A random variable that can take on any value within a certain range or interval. These variables are typically measured and can include decimals or fractions. Examples of continuous random variables include height, weight, or time, as in the case of how long an individual watches television.
Now, let's apply this understanding to the given item. The amount of time an individual watches television can be measured in hours, minutes, or even seconds. It can take on any value within a range, such as 1.5 hours, 3.25 hours, or 4.78 hours. Since time can be measured at any decimal point, it falls into the category of continuous random variables.
Therefore, the correct answer is c. Continuous random variable.