document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=259167>Question 259167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Chebyshev’s theorem to find what percent of the values will<BR>\n" );
document.write( "fall between 10 and 26 for a data set with mean of 18 and standard<BR>\n" );
document.write( "deviation of 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the Empirical Rule to find what two values 99.7% of the data<BR>\n" );
document.write( "will fall between for a data set with mean 0 and standard deviation<BR>\n" );
document.write( "of 12. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190827 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=190827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use Chebyshev’s theorem to find what percent of the values will<BR>\n" );
document.write( "fall between 10 and 26 for a data set with mean of 18 and standard<BR>\n" );
document.write( "deviation of 2.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "10 is (10-18)/2 = -4 standard deviations to the left of the mean.<BR>\n" );
document.write( "28 is (26-18)/2 = +4 standard deviations to the right of the mean.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Chebyshev says \"at least [1-(1/4)^2] = 15/16 of the data lies in<BR>\n" );
document.write( "that interval. <BR>\n" );
document.write( "15/16 = 93.75%<BR>\n" );
document.write( "---------------------------- \r<BR>\n" );
document.write( "\n" );
document.write( "Use the Empirical Rule to find what two values 99.7% of the data<BR>\n" );
document.write( "will fall between for a data set with mean 0 and standard deviation<BR>\n" );
document.write( "of 12.<BR>\n" );
document.write( "If 1-(1/k)^2 = 0.997, solve for \"k\".<BR>\n" );
document.write( "(1/k)^2 = 0.003<BR>\n" );
document.write( "1/k = 0.05477...<BR>\n" );
document.write( "k = 18.257 (number of standard deviations to the right and to the left of zero)<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "18.257*12 = 219.09<BR>\n" );
document.write( "----<BR>\n" );
document.write( "99.7% of the data is between -219.09 and +219.09<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );