<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/technology/cnxml/schema/dtd/0.5/cnxml_mathml.dtd">
<document xmlns="http://cnx.rice.edu/cnxml" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" xmlns:m="http://www.w3.org/1998/Math/MathML" id="new">
  <name>Normal Distribution: Areas to the Left and Right of x</name>
  <metadata>
  <md:version>1.4</md:version>
  <md:created>2008/06/06 14:39:08 GMT-5</md:created>
  <md:revised>2008/07/21 03:01:19.622 GMT-5</md:revised>
  <md:authorlist>
      <md:author id="billowsky">
      <md:firstname>Barbara</md:firstname>
      
      <md:surname>Illowsky</md:surname>
      <md:email>illowskybarbara@deanza.edu</md:email>
    </md:author>
      <md:author id="sdean">
      <md:firstname>Susan</md:firstname>
      
      <md:surname>Dean</md:surname>
      <md:email>deansusan@deanza.edu</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="cnxorg">
      <md:firstname/>
      
      <md:surname>Connexions</md:surname>
      <md:email>cnx@cnx.org</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>elementary</md:keyword>
    <md:keyword>statistics</md:keyword>
  </md:keywordlist>

  <md:abstract/>
</metadata>
  <content>
    <para id="delete_me">The arrow in the graph below points to the area to the left of <m:math><m:mi>x</m:mi></m:math>. This area is
represented by the probability 
<emphasis>
<m:math>
<m:reln><m:lt/>
<m:mrow>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
</m:math>. 
</emphasis>
Normal tables, computers, and calculators
provide or calculate the probability 
<m:math>
<m:reln><m:lt/>
<m:mrow>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
</m:math>.</para><para id="element-741"><media type="image/png" src="normdist_arealrx1.png">
<param name="alt" value="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."/>

<param name="print-width" value="3in"/>
</media></para><para id="element-97"><emphasis>
The area to the right is then
<m:math>
<m:reln><m:gt/>
<m:mrow>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
<m:mo>=</m:mo>
<m:reln><m:lt/>
<m:mrow>
<m:mn>1</m:mn>
<m:mo>-</m:mo>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
</m:math>.
</emphasis></para><para id="element-521">Remember, 
<m:math>
<m:reln><m:lt/>
<m:mrow>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
<m:mo>=</m:mo>
</m:math>

<emphasis>Area to the left</emphasis> of the vertical line through <m:math><m:mi>x</m:mi></m:math>.</para><para id="element-732"><m:math>
<m:reln><m:gt/>
<m:mrow>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
<m:mo>=</m:mo>
<m:reln><m:lt/>
<m:mrow>
<m:mn>1</m:mn>
<m:mo>-</m:mo>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
<m:mo>=</m:mo>
</m:math>.
<emphasis>Area to the right</emphasis>
of the vertical line through <m:math><m:mi>x</m:mi></m:math></para><para id="element-974"><m:math>
<m:reln><m:lt/>
<m:mrow>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
</m:math>
is the same as
 <m:math>
<m:reln><m:leq/>
<m:mrow>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
</m:math>
and
 <m:math>
<m:reln><m:gt/>
<m:mrow>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
</m:math>
is the same as
 <m:math>
<m:reln><m:geq/>
<m:mrow>
<m:mi>P</m:mi>
<m:mo>(</m:mo>
<m:mi>X</m:mi>
</m:mrow>
<m:mrow>
<m:mi>x</m:mi>
<m:mo>)</m:mo>
</m:mrow>
</m:reln>
</m:math>
for continuous distributions.</para>   
  </content>
  
</document>
