With a PDF, probabilities are calculated by finding areas ___________ ____ ________.

With a PDF, probabilities are calculated by finding areas ___________ ____ ________.

• A. under the curve
• B. above the curve
• C. to the left of the curve
• D. on the curve

Answer: (A)

For a probability density function, probabilities come from the area under the curve between the values of interest. The height of the curve gives density, not probability, so you integrate f(x) over the interval to get P(a ≤ X ≤ b). Geometrically, that integral is the area under the PDF between a and b, and the total area under the entire curve equals 1, reflecting total probability. So the correct description is the area under the curve. If you think about the other statements: areas above the curve aren’t how probabilities are computed from a PDF, and the idea of areas to the left of the curve isn’t the standard form for a single continuous variable’s probability. And a single point on a continuous distribution has probability zero, since it corresponds to area on a curve with zero width.

For a probability density function, probabilities come from the area under the curve between the values of interest. The height of the curve gives density, not probability, so you integrate f(x) over the interval to get P(a ≤ X ≤ b). Geometrically, that integral is the area under the PDF between a and b, and the total area under the entire curve equals 1, reflecting total probability. So the correct description is the area under the curve.

If you think about the other statements: areas above the curve aren’t how probabilities are computed from a PDF, and the idea of areas to the left of the curve isn’t the standard form for a single continuous variable’s probability. And a single point on a continuous distribution has probability zero, since it corresponds to area on a curve with zero width.