document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=831516>Question 831516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A data distribution has a mean of 100 and a standard deviation of 10. Assume that the shape of the distribution is unknown.\r<BR>\n" );
document.write( "\n" );
document.write( "The proportion of the data that falls between 80 and 120 is at least ___ percent. (Give your answer as a whole number.)\r<BR>\n" );
document.write( "\n" );
document.write( "I put 95 and it said it was wrong, I'm at a loss. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #501497 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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/cgi-bin/show-face.mpl?user=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=501497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:<BR>\n" );
document.write( "A data distribution has a mean of 100 and a standard deviation of 10. Assume that the shape of the distribution is unknown.\r<BR>\n" );
document.write( "\n" );
document.write( "The proportion of the data that falls between 80 and 120 is at least ___ percent. (Give your answer as a whole number.)<BR>\n" );
document.write( "-------------------------------------------------<BR>\n" );
document.write( "A:<BR>\n" );
document.write( "80 = 2 standard deviations below the mean<BR>\n" );
document.write( "100 = 2 standard deviations above the mean<BR>\n" );
document.write( "The proportion is 95% if the shape of the distribution is Normal.<BR>\n" );
document.write( "Since we don't know the shape of distribution, we use Chebyshev Inequality to get the lower bound for proportion.<BR>\n" );
document.write( "Using Chebyshev Inequality, the proportion is at least<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+1%2F%282%5E2%29 ALIGN=MIDDLE  ALT=\"1+-+1%2F%282%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2875%29 ALIGN=MIDDLE  ALT=\"highlight%2875%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > percent </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );