Question

decide whether the random variable x is discrete or continuous. explain your reasoning.

let x represent the time it takes to run a mile.

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

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

Explanation:

Analyze the nature of the variable

The random variable \(x\) represents the time it takes to run a mile. Time is a measurement that can take on any value within an interval, rather than a set of distinct, countable values.

Classify the random variable

Because the possible values of \(x\) cannot be listed or counted (they form an interval of real numbers), \(x\) is classified as a continuous random variable.

Answer:

• A. Discrete, because x is a random variable that can be counted.
• B. Continuous, because x is a random variable that cannot be counted. (Correct answer)