document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167991>Question 1167991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.\r<BR>\n" );
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document.write( "The shaded area is on the right of the curve. It is X=0.1753.\r<BR>\n" );
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document.write( "I need the Z score and use the z score to find the indicated IQ score. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792595 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean is 100 and the standard deviation is 15.\r<BR>\n" );
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document.write( "the shaded area on the right of the distribution curve represents an area of .1753 * the area under the normal distribution curve.\r<BR>\n" );
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document.write( "the area under the normal distributive curve is equal to 1.\r<BR>\n" );
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document.write( "the 1 represents 100% of the area under the normal distribution curve.\r<BR>\n" );
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document.write( "the .1753 represents 17.53% of the area under the normal distribution curve.\r<BR>\n" );
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document.write( "you are looking for a z-score that has an area of .1753 to the right of it.\r<BR>\n" );
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document.write( "subtract that from 1 and you are looking for a z-score that has an area of .8247 to the left of it.\r<BR>\n" );
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document.write( "a z-score calculator helps here.\r<BR>\n" );
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document.write( "the one that i have on my ti-84 plus calculator tells me that a z-score with an area of .8247 to the left of it is equal to .9334 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "graphically, this looks like the following.\r<BR>\n" );
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document.write( "the first graph shows the z-score with an area to the left of it of .8247.\r<BR>\n" );
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document.write( "the second graph shows the z-score with an area to the right of it of .1753\r<BR>\n" );
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document.write( "it's the same z-score of .9334.\r<BR>\n" );
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document.write( "this confirms that the area to the right of the z-score is equal to 1 minus the area to the left of it.\r<BR>\n" );
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document.write( "this also confirms that the area to the left of the z-score is equal to 1 minus the area to the right of it.\r<BR>\n" );
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document.write( "if you have one, you can get the other one by taking 1 minus the area.\r<BR>\n" );
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document.write( "now that you know the z-score, you can solve for the raw score.\r<BR>\n" );
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document.write( "your mean is 100 and your standard deviation is 15.\r<BR>\n" );
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document.write( "the z-score formula is:\r<BR>\n" );
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document.write( "z = (x - m) / s\r<BR>\n" );
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document.write( "z is the z-score.<BR>\n" );
document.write( "x is the raw score.<BR>\n" );
document.write( "m is the raw mean.<BR>\n" );
document.write( "s can be the standard deviation or the standard error.<BR>\n" );
document.write( "in this case, s represents the standard deviation.\r<BR>\n" );
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document.write( "when the z-score is .9334, and the mean is 100 and the standard deviation is 15, the z-score formula becomes:\r<BR>\n" );
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document.write( ".9334 = (x - 100) / 15\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = .9334 * 15 + 100 = 114.001\r<BR>\n" );
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document.write( "that's your raw score.\r<BR>\n" );
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document.write( "that means that the IQ score that has .1753 * the area under the normal distribution curve to the right of it is equal to 114.001\r<BR>\n" );
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document.write( "it also means that the IQ score that has .8247 * the area under the normal distribution curve to the left of it is equal to 114.001.\r<BR>\n" );
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document.write( "this can be seen in the following two displays.\r<BR>\n" );
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document.write( "the first display shows the area to the right of the indicated IQ.\r<BR>\n" );
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document.write( "the second display shows the area to the left of the indicated IQ.\r<BR>\n" );
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document.write( "the IQ is the same in both cases, as it should be because the area to the right of the indicated IQ score is equal to 1 minus the area to the left of the indicated IQ score, and vice versa.\r<BR>\n" );
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document.write( "your solution is that the IQ score that has an area of .1753 * the area under the normal distribution curve is 114.001.\r<BR>\n" );
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document.write( "once again, the complete area under the normal distribution curve is assumed to be 1.\r<BR>\n" );
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document.write( "the normal z-score calculator that was used to provide these displays can be found at <a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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