document.write( "Question 186072This question is from textbook Elementary Statistics
\n" ); document.write( ": I just can't figure this problem out ... totally lost ...\r
\n" ); document.write( "\n" ); document.write( "For a certain type of job, it costs a company an average of $231 to train an employee to perform the task. The standard deviation is $5. Find the minimum percentage of data values that will fall in the range of $219 to $243. Use Chebyshev's theorem.\r
\n" ); document.write( "\n" ); document.write( "I began by identifying the $5 std deviation;
\n" ); document.write( "From there I took the sum of $219 to $234 (range) and spread the range by 5 std devs per range ... 219 224 229 234 239 244 ...
\n" ); document.write( "at this point, I'm stumped ... this is from my 2nd class and I have 10 more to go so I've gotta understand this and I don't. Please help.
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Algebra.Com's Answer #139580 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Mean = $231\r\n" );
document.write( "Standard deviation = $5\r\n" );
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document.write( "Long ago, a Russian mathematician named\r\n" );
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document.write( "Пафну́тий Льво́вич Чебышёв\r\n" );
document.write( "Pafnuty Lvovich Chebyshev (1821-1894)\r\n" );
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document.write( "came up with a formula for finding what percentage of any set \r\n" );
document.write( "of numbers must lie close to the mean.\r\n" );
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document.write( "In particular for any positive number k, the percentage of the \r\n" );
document.write( "data that lies within k standard deviations of the mean is at \r\n" );
document.write( "least  changed to a percent.\r\n" );
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document.write( "First we need to find out how many standard deviations $219 and \r\n" );
document.write( "$243 are from the mean of $231.  We subtract to find which, if \r\n" );
document.write( "either, of the two bounds, $219 and $234, is closer to the mean. \r\n" );
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document.write( "$231-$219=$12\r\n" );
document.write( "$243-$231=$12\r\n" );
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document.write( "(If those hadn't been the same we would have picked the smaller.)\r\n" );
document.write( "we find that both limits are $12 from the mean.  Now we want to see\r\n" );
document.write( "how many standard deviations this $12 difference is.  So we divide\r\n" );
document.write( "by the given standard deviation, $5, to find out:\r\n" );
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document.write( "$12÷$5 = 2.4 = k standard deviations from the mean\r\n" );
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document.write( "So we want to know at least what percentage of the data must fall\r\n" );
document.write( "within 2.4 standard deviations of the mean.  So we plug 2.4 for k\r\n" );
document.write( "in Chebyshev's formula:\r\n" );
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document.write( "Now we change that to a percent.  So at least 82.6% of the data \r\n" );
document.write( "must fall within 2.4 standard deviations of the mean, and that \r\n" );
document.write( "tells us that at least 82.6% of the data must fall between \r\n" );
document.write( "$219 and $243.\r\n" );
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document.write( "Edwin

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