document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894078>Question 894078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem :  <BR>\n" );
document.write( "A set of examination marks are normally distributed with a mean of 75 and standard deviation of 5. If the top 5% of students got grade A and the bottom 25% got grade F. Then what is the lowest mark for A and the highest mark for F\r<BR>\n" );
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document.write( "Thanks in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #541735 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=541735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you need to find the z-score that has 5% of the area under the normal distribution curve to the right of it.\r<BR>\n" );
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document.write( "you also need to find the z-score that has 25% of the area under the normal distribution curve to the left of it.\r<BR>\n" );
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document.write( "you can use a z-score table or you can use a z-score calculator.\r<BR>\n" );
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document.write( "the best calculator i've been able to find is at the following link:\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( "this calculator takes all the drudgery out of finding the z-score or finding the area to the left or right of a given area.\r<BR>\n" );
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document.write( "not only does it show you the z-score, but it also shows you a picture of the normal distribution curve and where under that your desired area lies.\r<BR>\n" );
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document.write( "using this calculator, i found that the z-score that had 5% of the area under the normal distribution curve to the right of it is 1.645.\r<BR>\n" );
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document.write( "here's a picture of what the calculator showed me.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/082101.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "i also found that the z-score that had 25% of the area under the normal distribution curve to the left of it is -.674\r<BR>\n" );
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document.write( "here's a picture of what the calculator showed me.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/082102.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you now need to translate the z-score to a raw score.\r<BR>\n" );
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document.write( "the formula for z-score 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 population mean.<BR>\n" );
document.write( "s, in this case, is the population standard deviation since you are not dealing with a sample but are dealing with the poopulation itself.\r<BR>\n" );
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document.write( "since you are solving for the raw score, you need to modify the formula to solve for x rather than z\r<BR>\n" );
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document.write( "start with z = (x-m) / s<BR>\n" );
document.write( "multiply both sides of this equation by s to get:<BR>\n" );
document.write( "z*s = x-m<BR>\n" );
document.write( "add m to both sides of this equation to get:<BR>\n" );
document.write( "z*s + m = x<BR>\n" );
document.write( "slip sides to get:<BR>\n" );
document.write( "x = z*s + m\r<BR>\n" );
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document.write( "that's  the formula you need to find the raw score.\r<BR>\n" );
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document.write( "x = z*s + m\r<BR>\n" );
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document.write( "x is what you want to find.<BR>\n" );
document.write( "z is equal to 1.645 or -.674.<BR>\n" );
document.write( "s is equal to 5<BR>\n" );
document.write( "m is equal to 75\r<BR>\n" );
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document.write( "let's find the raw score associated with a z score of 1.645\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "x = 1.645 * 5 + 75 which results in:\r<BR>\n" );
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document.write( "x = 83.225\r<BR>\n" );
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document.write( "let's find the raw scire assicuated with a z score of -.674\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "x = -.674 * 5 + 75 which results in:\r<BR>\n" );
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document.write( "x = 71.63\r<BR>\n" );
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document.write( "if you get a score below 71.63, you will be in the bottom 25% of the students who took the test.\r<BR>\n" );
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document.write( "if you get a score above 83.225, you will be in the top 5% of the students who took the test.\r<BR>\n" );
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document.write( "the z score calculator is so good, you could also have used the raw score rather than the z score.\r<BR>\n" );
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document.write( "i didn't show you how to do that because i wanted to deal with z scores which is what you have to deal with anyway.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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