Final answer:
False. The number of defective pencils in a lot of 1000 is a discrete random variable, as it can be counted and will result in a whole number. Continuous random variables are measurable, taking on an infinite number of values within a range, an example being temperature or height.
Step-by-step explanation:
The statement that the number of defective pencils in a lot of 1000 is an example of a continuous random variable is false. This is an example of a discrete random variable. The number of defective pencils can be counted and will result in a whole number, which falls under the category of discrete data. A continuous random variable, on the other hand, involves outcomes that are not countable but are measurable and can take on any value within an interval. Examples of continuous random variables include temperature, weight, height, and monetary amounts.
In summary, continuous random variables require measurement and can take on an infinite number of possible values within a range. Since the number of defective pencils can only be expressed as a whole number, it is definitively classified as a discrete random variable. To understand the concept of continuous random variables better, consider examples like the temperature of a day or the height of an individual, which can vary continuously.