document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183149>Question 1183149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"A study of the nicotine contents of a certain brand of cigarette shows that on the average, one cigarette contains 1.52 milligrams of nicotine with a standard deviation of 0.07 milligrams\". Between what values must the nicotine content be for: (Hint: Use Chebyshev’s Theorem)							<BR>\n" );
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document.write( "a. At least 24/25 of all cigarettes of this brand?								<BR>\n" );
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document.write( "b. At least 48/49 of all cigarettes of this brand?								<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813363 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=813363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > represent the random variable for the nicotine content of a cigarette.\r<BR>\n" );
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document.write( "Then Chebyshev's theorem states that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28abs%28X+-+mu%29+%3C=+k%2Asigma%29+=+P%28abs%28X+-+1.52%29+%3C=+0.07k%29%3E=+1-1%2Fk%5E2 ALIGN=MIDDLE  ALT=\"P%28abs%28X+-+mu%29+%3C=+k%2Asigma%29+=+P%28abs%28X+-+1.52%29+%3C=+0.07k%29%3E=+1-1%2Fk%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "a.  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1%2Fk%5E2+=+24%2F25 ALIGN=MIDDLE  ALT=\"1-1%2Fk%5E2+=+24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2+=+25 ALIGN=MIDDLE  ALT=\"k%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   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+-+1.52%29+%3C=+0.07%2A5+=+0.35 ALIGN=MIDDLE  ALT=\"abs%28X+-+1.52%29+%3C=+0.07%2A5+=+0.35\"   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=-0.35+%3C=+X+-+1.52+%3C=+0.35 ALIGN=MIDDLE  ALT=\"-0.35+%3C=+X+-+1.52+%3C=+0.35\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.17+%3C=+X+%3C=+1.87 ALIGN=MIDDLE  ALT=\"1.17+%3C=+X+%3C=+1.87\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "b.  Apply the same procedure as in part (a), but now letting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1%2Fk%5E2+=+48%2F49 ALIGN=MIDDLE  ALT=\"1-1%2Fk%5E2+=+48%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+7 ALIGN=MIDDLE  ALT=\"k+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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