document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=431234>Question 431234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The annual income of residents in a county is $42,000 with a standard deviation of $10,000.  Between what two values do 95% of the incomes of county residents lie? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #299350 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=299350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming a normal distribution, then by the empirical rule, 95% of the incomes lie within two standard deviations, or between $22,000 and $62,000.<BR>\n" );
document.write( "Assuming non-normality, and using Chebyshev's theorem, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28abs%28X+-+42000%29+%3C=+k%2A10000%29+%3E=+1-1%2Fk%5E2+=+0.95 ALIGN=MIDDLE  ALT=\"P%28abs%28X+-+42000%29+%3C=+k%2A10000%29+%3E=+1-1%2Fk%5E2+=+0.95\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fk%5E2+=+0.05 ALIGN=MIDDLE  ALT=\"1%2Fk%5E2+=+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+2sqrt%285%29 ALIGN=MIDDLE  ALT=\"k+=+2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28X+-+42000%29+%3C=+20000sqrt%285%29 ALIGN=MIDDLE  ALT=\"abs%28X+-+42000%29+%3C=+20000sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42000+-++20000sqrt%285%29%3C=+X+%3C=++42000+%2B+20000sqrt%285%29 ALIGN=MIDDLE  ALT=\"42000+-++20000sqrt%285%29%3C=+X+%3C=++42000+%2B+20000sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the left endpoint is negative, the bounds are 0 and 86,721.36. </SPAN>\n" );
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