document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=397411>Question 397411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using Chebyshev's theorm find what percent of the values will fall between 175 and 241 for a data set with a mean of 208 and standard deviation of 11.\r<BR>\n" );
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document.write( "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 245 and standard deviation of 16.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #281751 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=281751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Chebyshev's Theorem states that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28abs%28X+-+mu%29+%3C+k%2Asigma%29+%3E=+1+-+1%2Fk%5E2 ALIGN=MIDDLE  ALT=\"P%28abs%28X+-+mu%29+%3C+k%2Asigma%29+%3E=+1+-+1%2Fk%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+208 ALIGN=MIDDLE  ALT=\"mu+=+208\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma+=+11 ALIGN=MIDDLE  ALT=\"sigma+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28175+%3C+X+%3C+241%29=%0D%0AP%28abs%28X+-+208%29+%3C+3%2A11+=+33%29+%3E=+1+-+1%2F9+=+8%2F9 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.  Hence at least <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F9%29%2A100+=+88.89 ALIGN=MIDDLE  ALT=\"%288%2F9%29%2A100+=+88.89\"   DISABLED_style= \"max-width:90%; height:auto;\" >% of the values will fall between 175 and 241.\r<BR>\n" );
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document.write( "The Empirical rule, or the 68-95-99.7 rule, says that 99.7% of the values lie within 3 standard deviations of the mean, given that the values are NORMALLY distributed.  Hence around 99.7% of all values would fall between 175 and 241. </SPAN>\n" );
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