Skip to content Skip to navigation


You are here: Home » Content » Normal Distribution: Areas to the Left and Right of x


Recently Viewed

This feature requires Javascript to be enabled.


(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

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.

Content actions

Download module as:

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens


A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks