document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153088>Question 1153088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph illustrates the distribution of test scores taken by College Algebra students. The maximum possible score on the test was 140, while the mean score was 78 and the standard deviation was 15.\r<BR>\n" );
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document.write( "33 - 48 - 63 - 78 in the middle - 93 - 108 - 123<BR>\n" );
document.write( "Distribution of Test Scores<BR>\n" );
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document.write( "What is the approximate percentage students who scored between 63 and 93 on the test?<BR>\n" );
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document.write( "What is the approximate percentage of students who scored between 48 and 108 on the test?<BR>\n" );
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document.write( "What is the approximate percentage of students who scored between 78 and 123 on the test?<BR>\n" );
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document.write( "What is the approximate percentage of students who scored higher than 123 on the test?<BR>\n" );
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document.write( "I would like to know how to solve, thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775366 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=775366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you use the following calculator, you can solve this fairly easily.\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( "in this calculator, if you work from the raw scores, you give it the mean the standard deviation and you answer the questions in the area from a value section.\r<BR>\n" );
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document.write( "here's your display of answers working from raw scores.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/022901.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/022904.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "if you work from z-scores, you give it the mean of 0 and the standard deviation of 1.\r<BR>\n" );
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document.write( "you will then get the z-score and you will then translate them to the raw scores.\r<BR>\n" );
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document.write( "for example, i will do one of these working from the z-score.\r<BR>\n" );
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document.write( "What is the approximate percentage students who scored between 63 and 93 on the test?\r<BR>\n" );
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document.write( "to work from z-scores, translate the raw score to z-score using the z-score formula of z = (x - m) / s<BR>\n" );
document.write( "z is the z-score.<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw score mean<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "for the raw score of 63, you will get z = (63 - 78) / 15 = -1<BR>\n" );
document.write( "this means that the raw score of 63 is 1 standard deviation below the mean.\r<BR>\n" );
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document.write( "for the raw score of 93, you will get z = (93 - 78) / 15 = 1<BR>\n" );
document.write( "this means that the raw score of 93 is 1 standard deviation above the mean.\r<BR>\n" );
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document.write( "if you are working off the z-score tables, you will then look up a z-score of -1 and a z-score of 1.\r<BR>\n" );
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document.write( "you will find that the area to the left of a z-score of -1 is equal to .15866 and the area to the left of a z-score of 1 is equal to .84134\r<BR>\n" );
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document.write( "to find the area in between these two z-scores, subtract the smaller area from the large area to get .68268.\r<BR>\n" );
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document.write( "that's pretty close to the area of .6827 found using the online calculator.\r<BR>\n" );
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document.write( "if we used the online calculator with z-score rather than raw scores, the output for this particular example would look like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/022905.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the calculator gives you the area in between the two z-scores.\r<BR>\n" );
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document.write( "you need to manually translate the z-scores to raw scores using the z-score formula.\r<BR>\n" );
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document.write( "here's a copy of the z-score table for your referEnce.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf\" target = \"_blank\">https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf</a>\r<BR>\n" );
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