Question

Which of the following random variables are continuous?

I). the air pressure in an automobile tire (in pounds per square inch)
II). the diameter of an automobile tire (in centimeters)
III). the number of miles traveled by an automobile tire

Answer 1

The air pressure in a tire, the diameter of a tire, and the number of miles traveled by a tire can all be considered continuous random variables as they are measured in fine detail and can assume a wide range of values.

Step-by-step explanation:

In the given question, we are asked to identify which random variables are continuous. A continuous random variable is one that can take an infinite number of different values within a given range, and these values are usually obtained through measurement. In contrast, a discrete random variable can only take certain distinct values, typically whole numbers from counting.

1. The air pressure in an automobile tire (in pounds per square inch) is a continuous random variable because air pressure can be measured in infinitely fine increments and is not countable.
2. The diameter of an automobile tire (in centimeters) is also a continuous random variable since diameters can vary continuously and are measured rather than counted.
3. The number of miles traveled by an automobile tire, if considered precisely (to the nearest fraction of a mile or in decimals), would be a continuous random variable. However, if it is rounded to the nearest mile, it becomes a discrete random variable. Without further context assuming precise measurement, we can consider it continuous.

All three variables mentioned can be measured in fine detail, making them continuous in nature. Thus, each of them exhibits properties of a continuous random variable, reflecting a wide range of potential values.