document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170017>Question 1170017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A teacher gave a test on which the students' marks were normally distributed, but the results were pathetic. The mean was 52%, and the standard deviation was 12%. The teacher decided that the top 10% of the students should get A's, the next 20% should get B's, the next 40% should get C's, the next 20% should get D's, and the bottom 10% should get F's. To the nearest percent, what was the minimum percent a student had to achieve in order to recieve a B? Do not include the percent sign in your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794909 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=794909\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 52%<BR>\n" );
document.write( "standard deviation = 12%<BR>\n" );
document.write( "top 10% get A<BR>\n" );
document.write( "next 20% get B<BR>\n" );
document.write( "next 40% get C<BR>\n" );
document.write( "next 20% get D<BR>\n" );
document.write( "bottom 10% get F\r<BR>\n" );
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document.write( "minimum B score will be the z-score that has 10% + 20% = 30% of the area under the normal distribution curve to the right of it.\r<BR>\n" );
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document.write( "the table are set to calculate off of ratios, not percents.<BR>\n" );
document.write( "just divide the percent by 100 and you get an area of .30 to the right of the z-score.<BR>\n" );
document.write( "since the tables only look for area to the left of the z-score, you are looking for a z-score that has 1 - .30 = .70 of the area under the normal distribution curve to the left of it.\r<BR>\n" );
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document.write( "if you look in the z-score table,  you will find that a z-score of .52 has .69847 of the area under the normal distribution curve to the left of it and a z-score of .53 has .70194 of the area under the normal distribution curve to the left of it.\r<BR>\n" );
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document.write( "a manual interpolation leads to a z-score of .524409 rounded to 5 decimal digits.\r<BR>\n" );
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document.write( "that's pretty close to having an area of .7 to the left of it.\r<BR>\n" );
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document.write( "a check with an online calculator shows that a z-score of .524409 has an area of .7 to the left of it.\r<BR>\n" );
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document.write( "the display of the calculator results are shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/111807.jpg\" >\r<BR>\n" );
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document.write( "the calculator i used can be found at <a  rel=nofollow HREF= \"https://www.calculator.net/z-score-calculator.html?c1raw=3.075&c1mean=3.2&c1sd=.1&calctype=zscore&x=81&y=18\" target = \"_blank\">https://www.calculator.net/z-score-calculator.html?c1raw=3.075&c1mean=3.2&c1sd=.1&calctype=zscore&x=81&y=18</a>\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 deviation\r<BR>\n" );
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document.write( "the formula becomes .524409 = (x - 52) / 12.\r<BR>\n" );
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document.write( "solve for x to get x = .524409 * 12 + 52 = 58.292908.\r<BR>\n" );
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document.write( "that's the lowest score you can get and still get a B.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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