document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061625>Question 1061625</A>: <I><SPAN STYLE=\"word-break: break-all;\"> IQs are calibrated so that they have a mean of 100 and a standard deviation of 15.\r<BR>\n" );
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document.write( "a) Find the probability that a randomly selected person has an IQ between 106 and 116. Be sure to draw a sketch.\r<BR>\n" );
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document.write( "b) A person with an IQ at or below the 5th percentile is considered “developmentally disabled”. What IQ corresponds to the cutoff for this designation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677322 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=677322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the easiest way to figure this out is to use the following online statistical z-score calculator.\r<BR>\n" );
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document.write( "<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( "the probability that a randomly selected person has an IQ between 106 and 116 is shown below, using this calculator:\r<BR>\n" );
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document.write( "the answer shown is .2015\r<BR>\n" );
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document.write( "the IQ at or below the 5th percentile is shown below:\r<BR>\n" );
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document.write( "the answer shown is 75.322\r<BR>\n" );
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document.write( "this calculator allows you to analyze the distribution without having to translate to z-scores.\r<BR>\n" );
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document.write( "if you did have to translate to z-scores, you would have done the following, using the formula indicated.\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 mean<BR>\n" );
document.write( "s is the standared deviation.\r<BR>\n" );
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document.write( "in the first part of your problem, you would calculate two z-scores.\r<BR>\n" );
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document.write( "z1 is the low z-score of the range.<BR>\n" );
document.write( "z2 is the high z-score of the range.\r<BR>\n" );
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document.write( "you would have gotten:\r<BR>\n" );
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document.write( "z1 = (106-100)/15 = .4\r<BR>\n" );
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document.write( "z2= (116-100)/15 = 1.067\r<BR>\n" );
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document.write( "you would then look up the area on the distribution curve between these z-scores.\r<BR>\n" );
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document.write( "the same calculator, using z-scores rather than raw scores, would assist you to find the answer.\r<BR>\n" );
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document.write( "that would be shown below:\r<BR>\n" );
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document.write( "the4 answer is the same as before, i.e. = .2015\r<BR>\n" );
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document.write( "you would also use the same calculator using a mean of 0 and a standard deviation of 1 to finf the z-scpore associated with the fifth percentile of IQs.\r<BR>\n" );
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document.write( "that z-score would be -1.645 as shown below:\r<BR>\n" );
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document.write( "you would then find the raw score by using the z-score formula as below:\r<BR>\n" );
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document.write( "z = (x-m)/s\r<BR>\n" );
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document.write( "-1.645 = (x - 100) / 15\r<BR>\n" );
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document.write( "solve for x to get x = -1.645 * 15 + 100 which is equal to 75.325\r<BR>\n" );
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document.write( "any small difference is more then likely due to rounding.\r<BR>\n" );
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document.write( "the z-score is a normalized score.\r<BR>\n" );
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document.write( "the mean becomes 0 and the standard deviation becomes 1.\r<BR>\n" );
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document.write( "a z-score of 0 is the same as the mean of the raw score.<BR>\n" );
document.write( "a standard deviation of 1 is the same as the standard deviation of the raw score.\r<BR>\n" );
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document.write( "this means that a z-core is the same as a raw score of 100 in your problem, and a z-score of 1 is the same as a raw score of 115 in your problem, and a z-score of -1 is the same as a z-score of 85 in your problem.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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