document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146567>Question 1146567</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An English professor assigns letter grades on a test according to the following scheme.\r<BR>\n" );
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document.write( "A:  Top 13% of scores\r<BR>\n" );
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document.write( "B:  Scores below the top 13% and above the bottom 61%<BR>\n" );
document.write( "C:  Scores below the top 39% and above the bottom 22%<BR>\n" );
document.write( "D:  Scores below the top 78% and above the bottom 6%<BR>\n" );
document.write( "F:  Bottom 6% of scores\r<BR>\n" );
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document.write( "Scores on the test are normally distributed with a mean of 75.1 and a standard deviation of 9.1.  Find the numerical limits for a D grade.  Round your answers to the nearest whole number, if necessary. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #767849 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=767849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"Scores below the top 78% and above the bottom 6%\" is another way of saying scores between 6% and 22%.<BR>\n" );
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document.write( "The rest of the info given isn't needed.<BR>\n" );
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document.write( "First, we will find what the numerical score is for 22%.<BR>\n" );
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document.write( "Go to a z-table and find where the value is 0.22. (Or, the closest value that's below 0.22, since the question states these are scores BELOW 22%...or, as they put it, scores below the top 78%.)  The z-score where this occurs is -0.78. (**NOTE: The fact that the z-score is -0.78 and the question states 78% is purely coincidental.)<BR>\n" );
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document.write( "Plug this into the following formula:<BR>\n" );
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document.write( "(x - mean)/SD = -0.78<BR>\n" );
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document.write( "(x - 75.1)/9.1 = -0.78<BR>\n" );
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document.write( "Solve for x:<BR>\n" );
document.write( "(x - 75.1)/9.1 = -0.78<BR>\n" );
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document.write( "(-0.78)(9.1) = (x - 75.1)<BR>\n" );
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document.write( "-7.098 = x - 75.1<BR>\n" );
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document.write( "x = 68.002<BR>\n" );
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document.write( "So, the 22% score is 68 (rounded off).<BR>\n" );
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document.write( "Next, we will find what the numerical score is for 6%.<BR>\n" );
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document.write( "Go to a z-table and find where the value is 0.06. (Or, the closest value that's above 0.06, since the question states these are scores ABOVE 6%.)  The z-score where this occurs is -1.55.<BR>\n" );
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document.write( "Plug this into the following formula:<BR>\n" );
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document.write( "(x - mean)/SD = -1.55<BR>\n" );
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document.write( "(x - 75.1)/9.1 = -1.55<BR>\n" );
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document.write( "Solve for x:<BR>\n" );
document.write( "(x - 75.1)/9.1 = -1.55<BR>\n" );
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document.write( "(-1.55)(9.1) = (x - 75.1)<BR>\n" );
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document.write( "-14.105 = x - 75.1<BR>\n" );
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document.write( "x = 60.995<BR>\n" );
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document.write( "So, the 6% score is 61 (rounded off).<BR>\n" );
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document.write( "The numerical limits for a D grade are \"higher than 61 and less than 68.\" </SPAN>\n" );
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