Question

determine whether the random variable x is discrete or continuous. explain.

let x represent the time it takes to fly from city a to city b.

choose the correct answer below.

a. the random variable is discrete, because it has a countable number of possible outcomes.
b. the random variable is continuous, because it has an uncountable number of possible outcomes.
c. the random variable is continuous, because it has a countable number of possible outcomes.
d. the random variable is discrete, because it has an uncountable number of possible outcomes.

Explanation:

Analyze the nature of the variable

\(x\) represents flight time, which is a measurement of duration.

Determine countability of outcomes

Time can take any real value within an interval, meaning the set of possible outcomes is uncountable.

Classify the random variable

A random variable with an uncountable number of outcomes is continuous.

Answer:

• A. The random variable is discrete, because it has a countable number of possible outcomes.
• B. The random variable is continuous, because it has an uncountable number of possible outcomes. (Correct answer)
• C. The random variable is continuous, because it has a countable number of possible outcomes.
• D. The random variable is discrete, because it has an uncountable number of possible outcomes.