Final answer:
The lifetime of a battery is a continuous random variable because it can take on any value within a certain range.
Step-by-step explanation:
The lifetime of a battery can be considered as a continuous random variable.
This is because the lifetime of a battery can take on any value within a certain range, such as the number of hours or months it can function before it needs to be replaced or recharged.
For example, the useful life of a car battery can be measured in months, and it can last anywhere from a few months to several years. This continuous range of possible lifetimes makes the variable 'X', which represents the useful life of the battery, a continuous random variable.