document.write( "Question 1134236: Hi! Looking at my teachers notes, they do not make sense. I am also waiting on an emai from her for extra help, but I figure ask here as well since I’ve gotten help before and it does help reading this and asking my teacher. The question is:\r
\n" ); document.write( "\n" ); document.write( "A class of 28 students took a 100 point test. If the mean was 68, is it possible that 23 of the students got a score of 63 or lower?\r
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Algebra.Com's Answer #751556 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If the class of 28 students took a 100 point test and if the mean was 68, then the total points was 28*68 = 1904.\r\n" );
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document.write( "Let assume that for some 23 students their average score was 63 or lower - then the total score for these 23 students was 23*63 = 1449 or lower.\r\n" );
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document.write( "Hence, the difference is  1904 - 1449 = 455 or greater, and it is what the rest of 28-23 = 5 students get altogether.\r\n" );
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document.write( "Since \"455%2F5\" = 91 is less than 100,  there is NO CONTRADICTION, which means that the given outcome IS POSSIBLE.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Usually,  the problems of this kind are designed to get a contradiction and thus disprove the possibility.\r
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\n" ); document.write( "\n" ); document.write( "But in the given / (posted) case,  this hypothetical design / (\"solution strategy\")  does not work.\r
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\n" ); document.write( "\n" ); document.write( "INTERESTING  NOTICE / addition.\r
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\n" ); document.write( "\n" ); document.write( "If,  on the contrary,  I slightly change the problem formulation in this way\r
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document.write( "    A class of 28 students took a 90 point test. If the mean was 68, is it possible that 23 of the students got a score of 63 or lower?\r\n" );
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\n" ); document.write( "\n" ); document.write( "then the answer is  \"IT  IS  IMPOSSIBLE\",  and the proof is as follows:\r
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document.write( "    If the class of 28 students took a 90 point test and if the mean was 68, then the total points was 28*68 = 1904.\r\n" );
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document.write( "    Let assume that for some 23 students their average score was 63 or lower - then the total score for these 23 students was 23*63 = 1449 or lower.\r\n" );
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document.write( "    Hence, the difference is  1904 - 1449 = 455 or greater, and it is what the rest of 28-23 = 5 students get altogether.\r\n" );
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document.write( "    But  90*5 = 450  is LESS than 455,  so in the 90-point test 5 students CAN NOT obtain  455 points cumulatively.\r\n" );
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document.write( "    CONTRADICTION (!).\r\n" );
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document.write( "    Which proves that  IT  IS  IMPOSSIBLE  (!)\r\n" );
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