Introduction
The shaded area in the following graph indicates the area to the left of x. This area could represent the percentage of students scoring less than a particular grade on a final exam. This area is represented by the probability P(X x). Normal tables, computers, and calculators are used to provide or calculate the probability P(X x).
The area to the right is then P(X > x) = 1 – P(X x). Remember, P(X x) = Area to the left of the vertical line through x. P(X x) = 1 – P(X x) = Area to the right of the vertical line through x. P(X x) is the same as P(X ≤ x) and P(X > x) is the same as P(X ≥ x) for continuous distributions.
Suppose the graph above were to represent the percentage of students scoring less than 75 on a final exam, with this probability equal to 0.39. This would also indicate that the percentage of students scoring higher than 75 was equal to 1 minus 0.39 or 0.61.