document.write( "Question 1203212: A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 30 thousand miles and a standard deviation of 8 thousand miles. How many miles will be traveled by at least 75% of the trucks? \n" ); document.write( "

Algebra.Com's Answer #838627 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A trucking company determined that the distance traveled per truck per year is normally distributed,
\n" ); document.write( "with a mean of 30 thousand miles and a standard deviation of 8 thousand miles.
\n" ); document.write( "How many miles will be traveled by at least 75% of the trucks?
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\n" ); document.write( "\n" ); document.write( "As the problem is worded, printed, posted and presented, it is TOTAL, GLOBAL and FATAL $\"highlight%28highlight%28nonsense%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "This my statement means that this formulation is nonsensical and the problem CAN NOT be solved in this formulation.\r
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\n" ); document.write( "\n" ); document.write( "The fact that Theo produced some text, even with a figure, does not make this nonsense more sensical.\r
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\n" ); document.write( "\n" ); document.write( "If you want to create something sensical from this text, then the problem should sound THIS WAY:\r
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document.write( "    A trucking company determined that the distance traveled per truck per year is normally distributed, \r\n" );
document.write( "    with a mean of 30 thousand miles and a standard deviation of 8 thousand miles.\r\n" );
document.write( "    Let X denotes some distance  and let D(X) denotes the integral distance, traveled \r\n" );
document.write( "    by all the company's trucks altogether, that covered more than X miles each (individually).\r\n" );
document.write( "    Find the value  X  such that  D(X)  is  75%  of  D, the total integral distance,  \r\n" );
document.write( "    traveled by all the trucks of the company, altogether.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Do you like this bulky formulation or not, but it is the ONLY WAY (a-UNIQUE-WAY)
\n" ); document.write( "to make a sensible problem from the original nonsensical set of words.\r
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\n" ); document.write( "\n" ); document.write( " And if you accept this my formulation, then the solution is as follows.\r
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document.write( "For any X, D(X) is the area under the given (specified) normal curve on the right of z-mark X.\r\n" );
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document.write( "So, the problem (in modified formulation ) asks to find the value  in such away, \r\n" );
document.write( "that the area under the specified normal curve on the right of  is 75% = 0.75 \r\n" );
document.write( "of the total area under this curve, i.e. simply 0.75.\r\n" );
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document.write( "To find , we use the standard function invNorm\r\n" );
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document.write( "                         area   mean   SD    <<<---===  formatting pattern.\r\n" );
document.write( "     = invNorm(0.25, 30000, 8000).\r\n" );
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document.write( "I use the area value 0.25, because function invNorm accept the area on the left of the mark, and 0.25 = 1-0.75.\r\n" );
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document.write( "Thus, the  ANSWER  is   = 24604 miles.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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