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Normal Distribution: Areas to the Left and Right of x

Module by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

Summary: Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

Note: You are viewing an old version of this document. The latest version is available here.

The arrow in the graph below points to the area to the left of xx. This area is represented by the probability P ( X < x ) P ( X x ) . Normal tables, computers, and calculators provide or calculate the probability P ( X < x ) P ( X x ) .

Normal distribution curve with a x value on the x-axis. The x-axis is equal to X. A vertical upward line extends from point x to the curve and the probability area occurs from the beginning of the curve to point x.

The area to the right is then P ( X > x ) = 1 - P ( X < x ) P ( X x ) = 1 - P ( X x ) .

Remember, P ( X < x ) = P ( X x ) = Area to the left of the vertical line through xx.

P ( X > x ) = 1 - P ( X < x ) = P ( X x ) = 1 - P ( X x ) =. Area to the right of the vertical line through xx

P ( X < x ) P ( X x ) is the same as P ( X ≤ x ) P ( X x ) and P ( X > x ) P ( X x ) is the same as P ( X ≥ x ) P ( X x ) for continuous distributions.

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