What does a continuous distribution imply about the values of X?

A continuous distribution implies that the variable X can take any value within a specified range, which can include fractions and decimals, not just whole numbers. This means that there are infinitely many possible values for X within that range, allowing for a smooth transition between values rather than discrete jumps, which would be the case in a discrete distribution.

For example, in a normal distribution, which is a common type of continuous distribution, you could have values of X like 1.5, 2.3, 2.999, etc., all within a certain interval. The property of continuity is vital in various statistical analyses, such as calculating probabilities using calculus. In contrast, discrete distributions would limit X to specific, distinct outcomes, which does not provide the same flexibility.

Thus, selecting the option indicating that X can take any value within a range fits the definition of a continuous distribution perfectly.