<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/295e7848-ee29-4871-87ff-850ea040d992/6B74ABB7-7117-493E-9451-19207A16A0A7/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://janda.org/c10/Lectures/topic05/L15-Normal.htm" href="http://janda.org/c10/Lectures/topic05/L15-Normal.htm" style="font-size: 11px;">janda.org</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><CENTER><FONT size="+1" color="#ffffff"><B>Statistical Inference: Normal Distribution</B></FONT></CENTER></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><CENTER><FONT size="+1"><B>The Normal Distribution and Z-Scores</B></FONT></CENTER></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><DT> <HR /> <FONT face="Times, Times New Roman, Latin"><B>Special properties of the normal distribution:</B></FONT> </DT></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><DD><FONT face="Times, Times New Roman, Latin">Their shape is such that it</FONT> <DL> <DD><FONT face="Times, Times New Roman, Latin">Embraces <B>68.26</B>% of the cases within <B>1</B> s.d. around the mean.</FONT></DD> <DD><FONT face="Times, Times New Roman, Latin">Embraces <B>95.46</B>% of the cases within <B>2 </B>s.d. around the mean.</FONT></DD> <DD><FONT face="Times, Times New Roman, Latin">Embraces <B>99.74</B>% of the cases within <B>3</B> s.d. around the mean.</FONT></DD> </DL> </DD></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><DT> <HR /> <B>Using the Table of Areas under the Normal Curve: The z-score</B></DT></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><DD><FONT face="Times, Times New Roman, Latin">One determines the probability of occurrence of a random event in a normal distribution by consulting a </FONT><FONT face="Courier, Courier New">t</FONT><FONT face="Times New Roman, Times, serif">ables of areas under a normal curve (e.g., </FONT><FONT face="Times, Times New Roman, Latin">Table D.2, pp.702-705 in Kirk).</FONT> <DL> <DD><FONT face="Times, Times New Roman, Latin">Tables of the normal curve have a mean of 0 and a standard deviation of 1.</FONT></DD> <DD><FONT face="Times, Times New Roman, Latin">To use the table., you must convert your data to have a mean of 0 and standard deviation of 1.</FONT></DD> <DD><FONT face="Times, Times New Roman, Latin">This is done by transforming your raw values into z-scores, according to this formula:</FONT> <BLOCKQUOTE><BLOCKQUOTE><DL> <DD>z-score = <IMG height="56" border="0" width="102" align="middle" src="http://janda.org/c10/Lectures/topic05/../../images/z-score.giF" /></DD> </DL> </BLOCKQUOTE></BLOCKQUOTE></DD> </DL> </DD></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><P><FONT face="Times New Roman, Times, serif"><B>Example: percent black in Washington, D.C. in 1980</B> (Note: not 1990)</FONT></P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><table background="undefined" bgcolor="#ffffcc"><tr><TD width="154" rowspan="2"><P align="right">60 / 12.5 = 4.8</p> </TD></tr></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><P><FONT face="Times New Roman, Times, serif"><B>z-score</B> for D.C. = <B>4.8</B></FONT></P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://janda.org/c10/Lectures/topic05/L15-Normal.htm"><div align="center"><img src="http://content9.clipmarks.com/blog_cache/janda.org/img/674F3E1E-FE3D-486F-A54E-923A2C6C0817" alt="" /></div></blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/6B74ABB7-7117-493E-9451-19207A16A0A7/blog/" title="blog or email this clip"><img src="http://content6.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>

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