document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136027>Question 1136027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ON A HW ASSIGNMENT THE MEAN SCORE WAS 85% WITH A STANDARD DEVIATION OF 4. WHAT ARE THE RAW SCORES FOR EACH OF THE FOLLOWING SCORES? -0.7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #753796 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=753796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 85 and standard deviation is 4.\r<BR>\n" );
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document.write( "formula for z-score is 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 raw mean<BR>\n" );
document.write( "s is the standard deviation\r<BR>\n" );
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document.write( "formula becomes -.7 = (x - 85) / 4\r<BR>\n" );
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document.write( "solve for x to get x = -.7 * 4 + 85\r<BR>\n" );
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document.write( "solve for x to get x = -2.8 + 85 = 82.2\r<BR>\n" );
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document.write( "the raw score associated with a z-score of -.7 when the mean is 85 and the standard deviation is 4 is equal to 82.2.\r<BR>\n" );
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document.write( "here's a visual representation of that.\r<BR>\n" );
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document.write( "the first graph shows the area under the normal distribution curve to the left of a raw score of 82.2 when the mean is 85 and the standard deviation is 4.\r<BR>\n" );
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document.write( "the second graph shows the area under the normal distribuion curve to the left of a z-score of -.7 when the mean is 0 and the standard deviation is 1.\r<BR>\n" );
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document.write( "the same area to the left of it means the raw score and the z-score have the same relative position under the normal distribution curve.\r<BR>\n" );
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document.write( "the z-score itself is telling you how many standard deviations you are away from the mean.\r<BR>\n" );
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document.write( "a z-score of -.7 means that you are .7 standard deviations to the left of the mean.\r<BR>\n" );
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document.write( "if your mean is 85 and your raw score is 82.2 and your standard deviation is 4, then then the difference is -2.8.\r<BR>\n" );
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document.write( "to find out how many standard deviations that is from the mean, you divide by the standard deviation to get -2.8 / 4 = -.7\r<BR>\n" );
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document.write( "here's the graphs.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/030501.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src= \"http://theo.x10hosting.com/2019/030502.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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