document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169930>Question 1169930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On an examination the average grade was 74 and the standard deviation was 7. If 12% of the class are given A's and 30% of the class given B's if the grades are curved to follow a normal distribution,<BR>\n" );
document.write( "a)What is the lowest possible A's Marks.<BR>\n" );
document.write( "b)What is the highest and lowest possible B's Marks.<BR>\n" );
document.write( "Answers:<BR>\n" );
document.write( "a)83 marks<BR>\n" );
document.write( "b)82 and 75 marks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794767 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=794767\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you round your z-scores to 3 decimal digits, you should get the answers to match.\r<BR>\n" );
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document.write( "if you use the normal distribution tables, you will need to the find the area to the left of the indicated z-score.\r<BR>\n" );
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document.write( "that's just the way the tables work.\r<BR>\n" );
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document.write( "i used a calculator, because the calculator is more accurate, but i made sure the z-score found was rounded to 3 decimal places before looking for the raw score.\r<BR>\n" );
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document.write( "the calculator makes the job easier because you don't have to manually interpolate to find the answer you are looking for.\r<BR>\n" );
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document.write( "to show you what's happening, the calculator i used can be found at <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( "while the calculator can find the answer more directly, i used the same method you would use if you were looking into the z-score tables.\r<BR>\n" );
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document.write( "your problem states:\r<BR>\n" );
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document.write( "On an examination the average grade was 74 and the standard deviation was 7. If 12% of the class are given A's and 30% of the class given B's if the grades are curved to follow a normal distribution,<BR>\n" );
document.write( "a)What is the lowest possible A's Marks.<BR>\n" );
document.write( "b)What is the highest and lowest possible B's Marks.<BR>\n" );
document.write( "Answers:<BR>\n" );
document.write( "a)83 marks<BR>\n" );
document.write( "b)82 and 75 marks.\r<BR>\n" );
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document.write( "you'll be looking for the z-score first and then translating to the raw score.<BR>\n" );
document.write( "the calculator can work directly from the raw scores but we won't do that because the tables work from z-scores only.\r<BR>\n" );
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document.write( "we'll do the A scorers first.\r<BR>\n" );
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document.write( "since A is the highest score and 12% of the class gets an A, then 88% of the class doesn't get an A.\r<BR>\n" );
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document.write( "you want to find the z-score that has an area of .88 to the left of it.\r<BR>\n" );
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document.write( "that z-score is 1.175 rounded to 3 decimal places.\r<BR>\n" );
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document.write( "here's the results of using the online calculator.\r<BR>\n" );
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document.write( "to find the equivalent raw score, you would use the z-score formula of:<BR>\n" );
document.write( "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( "mis the mean<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "since your mean is 74 and your standard deviation is 7, you would solve for the raw score as follows:\r<BR>\n" );
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document.write( "z-score formula becomes:<BR>\n" );
document.write( "1.175 = (x - 74) / 7<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 1.175 * 7 + 74 = 82.225.<BR>\n" );
document.write( "round up to the nearest integer to get 83.\r<BR>\n" );
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document.write( "we'll do the B scorers next.\r<BR>\n" );
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document.write( "the B scorers are below the A scorers and above the rest that aren't A or B.\r<BR>\n" );
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document.write( "the highest z-score for the B scorers will be the same as the lowest z-score for the A scorers.\r<BR>\n" );
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document.write( "that z-score is 1.175.\r<BR>\n" );
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document.write( "the difference here is you'll need to round down rather than up.\r<BR>\n" );
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document.write( "since the raw score was found to be 82.225, you will round down to 82.\r<BR>\n" );
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document.write( "the lowest z-score for the B scorers will be above 12% + 30% = 42% of the area under the normal distribution curve.\r<BR>\n" );
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document.write( "that's equivalent to being above 58% of the area under the normal distribution curve.\r<BR>\n" );
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document.write( "you are looking for an area of.58 to the left of the z-score.\r<BR>\n" );
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document.write( "you would use the calculator to get a z-score of .202.\r<BR>\n" );
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document.write( "here's the results of using the online calculator.\r<BR>\n" );
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document.write( "the raw score associated with a z-score of.202 is found using the z-score formula.\r<BR>\n" );
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document.write( "the formula of z = (x - m) / s becomes .202 = (x - 74) / 7.<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = .202 * 7 + 74 = 75.414.\r<BR>\n" );
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document.write( "round that up to 76.\r<BR>\n" );
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document.write( "the lowest score for a B scorer is 76 and the highest score for a B scorer is 82.\r<BR>\n" );
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document.write( "the answers they have are:\r<BR>\n" );
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document.write( "a) = 83<BR>\n" );
document.write( "b) = 82 and 75\r<BR>\n" );
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document.write( "the answers you have are:\r<BR>\n" );
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document.write( "a) = 83<BR>\n" );
document.write( "b) = 82 and 76\r<BR>\n" );
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document.write( "for the 75 score, i believe they rounded down when they should have rounded up.<BR>\n" );
document.write( "that's the difference.\r<BR>\n" );
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document.write( "a low score of 75 only has 56% of the area to the left of it.<BR>\n" );
document.write( "it's a small error, but it's an error.<BR>\n" );
document.write( "it should have had at least 58% of the area to the left of it.\r<BR>\n" );
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document.write( "a low score of 76 has 61% to the left of it.<BR>\n" );
document.write( "that's above 58% area to the left of it.\r<BR>\n" );
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document.write( "looks to me like they rounded correctly at the 88% mark, but botched it at the 58% mark.\r<BR>\n" );
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document.write( "for above 88%, they rounded up to 83 and for below 88% they rounded down to 82.\r<BR>\n" );
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document.write( "for above 58%, they should have rounded up to 76, but rounded down to 75 instead.\r<BR>\n" );
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document.write( "that's my opinion.\r<BR>\n" );
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document.write( "take it for what it's worth.\r<BR>\n" );
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document.write( "the procedure i used, however, is correct.\r<BR>\n" );
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document.write( "here's a picture i drew that will hopefully provide you with a visual of what's going on.\r<BR>\n" );
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document.write( "this can be a bit confusing, so if you have any questions, fire away.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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