A statistics student is studying continuous probability distributions. The student notices that when graphing a uniform distribution for a variable that ranges from 0 to 20, the graph forms a flat, rectangular shape. Why is the height of this rectangle always the same fixed value across the entire range?
- Because the total area under the curve equals zero for any single point, so the height must remain fixed to compensate.
- Because the height is determined by adding the minimum and maximum values together, producing a single uniform number.
- Because every value in the range is equally likely, the height is calculated as 1 divided by the total range (b − a), making it constant across all values.
- Because the curve must start high on the y-axis and decrease toward zero as x increases, creating a flat appearance.