document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119446>Question 1119446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A population of values has a normal distribution with &#956;=225.8 and &#963;=87.4. You intend to draw a random sample of size n=215.\r<BR>\n" );
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document.write( "Find P82, which is the mean separating the bottom 82% means from the top 18% means.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735063 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=735063\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population mean is 225.8<BR>\n" );
document.write( "population standard deviation is 87.4<BR>\n" );
document.write( "sample size is 215.\r<BR>\n" );
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document.write( "standard error = standard deviation divided by square root of sample size.\r<BR>\n" );
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document.write( "standard error = 87.4 / sqrt(215) = 5.960630527.\r<BR>\n" );
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document.write( "you look up in the normal distribution table, or use a normal distribution calculator, to find the z-score that is associated with 829% of the area under the normal distribution curve that is to the left of it.\r<BR>\n" );
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document.write( "i used the normal distribution calculator that is in the TI-84 Plus and came up with a z-score of .915365082.\r<BR>\n" );
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document.write( "to find the raw score associated with that, use the z-score formula of:\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 standard error.\r<BR>\n" );
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document.write( "that formula becomes:\r<BR>\n" );
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document.write( ".915365082 = (x-225.8) / 5.960630527.\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = .915365082 * 5.960630527 + 225.8.\r<BR>\n" );
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document.write( "that results in x = 231.2561531.\r<BR>\n" );
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document.write( "that score will have 82% of the normal distribution curve to the left of it and 18% of the normal distribution curve to the right of it.\r<BR>\n" );
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document.write( "that means the probability of getting a raw score less than 231.2561531 is 82% and the probability of getting a raw score greater than 231.2561531 is 18%.\r<BR>\n" );
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document.write( "visually, this looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/070601.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/070602.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the first display shows you the proability of getting a raw score less than 231.2561.\r<BR>\n" );
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document.write( "the second display shows you the probability of getting a raw score greater than 231.2561.\r<BR>\n" );
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document.write( "round your answer as required.\r<BR>\n" );
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document.write( "any difference between what this online calculator shows you and the calculator i used has to do how many decimal places rounding has occurred.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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