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How is the probability that a continuous random variable falls in an interval found from a density graph?

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

In probability theory, the probability that a continuous random variable falls within a specific interval is determined by the probability density function (PDF).

To find this probability from a density graph, you calculate the area under the curve of the function between the two values defining the interval. Specifically, if the random variable is denoted by X, the probability that X falls in an interval (a, b] is equal to the area under the graph of the density function f between a and b.12

The graph of a PDF is a curve positioned above the horizontal axis, where the total area between the curve and the axis is exactly 1. Because the probability corresponds to the area under the curve, the percentage of the total area included between any two points on the horizontal axis directly represents the probability that an observation will fall within that range.1