### 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.