Why is a person's weight modeled as a continuous random variable?

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sample space for a pair of dice — probability theory Sample space for a pair of dice.

A person's weight is modeled as a continuous random variable because it can take on an infinite number of possible values within a given range. Unlike discrete variables, which represent countable outcomes, weight is a measurement that can be subdivided infinitely; there is no smallest possible increment between two weights.

In probability theory, continuous variables are characterized by their ability to fall anywhere along a continuum. Because the number of potential outcomes is infinite, the probability of a person weighing an exact, precise value (e.g., exactly 70.000... kg) is technically zero. Instead, we use a density function to calculate the probability that a person's weight falls within a specific interval by computing the integral of that function over the range.1