Question

decide whether the random variable x is discrete or continuous. explain your reasoning.
let x represent the length of time it takes to run a mile.

is the random variable x discrete or continuous? choose the correct answer below.

a. continuous, because x is a random variable that cannot be counted.

b. discrete, because x is a random variable that can be counted.

Explanation:

To determine if the random variable \( x \) (time to run a mile) is discrete or continuous, we recall the definitions: Discrete variables take distinct, countable values (e.g., number of students), while continuous variables take any value in an interval (e.g., time, length) and are measured, not counted. Time to run a mile can be any value (e.g., 5.2 minutes, 7.8 seconds) and is not restricted to whole numbers, so it cannot be "counted" in the discrete sense. Option A states it is continuous because \( x \) cannot be counted, which matches the nature of time as a continuous variable. Option B is incorrect because time is not a countable (discrete) variable.

Answer:

A. Continuous, because x is a random variable that cannot be counted.