document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186035>Question 1186035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The results of the latest writing of the LSAT (Law School Aptitude Test) showed results that were normally distributed with a mean score of 829 and a standard deviation of 50.\r<BR>\n" );
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document.write( "The Osgoode Hall Law School wants candidates for admission to be in the top 1 <BR>\n" );
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document.write( "  of LSAT test scores. What is the minimum test score a candidate needs to achieve to be considered for admission to this school? \r<BR>\n" );
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document.write( "If a group of 42 applicants is randomly selected, what is the probability that the group average is not less than 849? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816953 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=816953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> men of the population is 829<BR>\n" );
document.write( "standard deviation of the population is 50.\r<BR>\n" );
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document.write( "critical z-score for admission to be in the top 1 percent is equal to 2.326348 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "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 individual score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation\r<BR>\n" );
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document.write( "the critical z-score formula becomes:\r<BR>\n" );
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document.write( "2.326348 = (x - 829) / 50.\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 2.326348 * 50 + 829 = 945.3174.\r<BR>\n" );
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document.write( "sample size = 42.\r<BR>\n" );
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document.write( "when you're dealing with the mean of a sample, rather than an individual score, you need to use the standard error.\r<BR>\n" );
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document.write( "standard error = standard deviation / square root of sample size = 50 / sqrt(42) = 7.715167 rounded to 6 decimal places.\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 sample mean<BR>\n" );
document.write( "m is the population mean<BR>\n" );
document.write( "s is the standard error\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "z = (849 - 829) / 7.715167 = 2.5923 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "area to the right of that z-score is equal to .00477 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "that's the probability that the group average is not less than 849.\r<BR>\n" );
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document.write( "i used the following calculator to confirm these results are accurate, assuming i calculated the standard error correctly.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.statskingdom.com/normal.html\" target = \"_blank\">https://www.statskingdom.com/normal.html</a>\r<BR>\n" );
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document.write( "the results from the use of that calculator are shown below.\r<BR>\n" );
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document.write( "minimum score for top 1%:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/101401.jpg\" >\r<BR>\n" );
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document.write( "probability of sample mean not less than 849.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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