document.write( "Question 664027: I. Use Chebyshev’s theorem to find what percent of the values will fall between 249 and 333 for a data set with a mean of 291 and standard deviation of 14.
\n" ); document.write( "
\n" ); document.write( "II. Use the Empirical Rule to find what two values 99.7% of the data will fall between for a data set with a mean of 219 and standard deviation of 20 \n" ); document.write( "
Algebra.Com's Answer #413188 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
I. Use Chebyshev’s theorem to find what percent of the values will fall between 249 and 333 for a data set with a mean of 291 and standard deviation of 14.
\n" ); document.write( "--------
\n" ); document.write( "(249-291)/14 = -3
\n" ); document.write( "(333-291)/14 = +3
\n" ); document.write( "----------------------------
\n" ); document.write( "The percent is at least 1-(1/3)^2 = 8/9 = 0.89 = 89% of the data.
\n" ); document.write( "======================================================================= \r
\n" ); document.write( "\n" ); document.write( "II. Use the Empirical Rule to find what two values 99.7% of the data will fall between for a data set with a mean of 219 and standard deviation of 20
\n" ); document.write( "--------
\n" ); document.write( "Solve 1 - (1/k)^2 = 0.997
\n" ); document.write( "----
\n" ); document.write( "= (1/k)^2 = 0.003
\n" ); document.write( "----
\n" ); document.write( "k^2 = 1/0.003
\n" ); document.write( "---
\n" ); document.write( "k^2 = 333.33
\n" ); document.write( "-----------------------
\n" ); document.write( "k = 18 +
\n" ); document.write( "---
\n" ); document.write( "lower limit: 219-18*20 = -141
\n" ); document.write( "upper limit: 219+18*20 = 579
\n" ); document.write( "=================================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "======================\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );