document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=484125>Question 484125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! Can someone please help me solve this problem:\r<BR>\n" );
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document.write( "A random sample of 50 gas stations in cook County, Illinois, result in a mean price per gallon of $1.60 and a standard deviation of $0.07.\r<BR>\n" );
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document.write( "a) determine the percentage of gas stations that have prices between $1.46 and $1.74, according to the Empirical Rule.\r<BR>\n" );
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document.write( "b) Determine the percentage of gas stations that have prices between $1.46 and $1.74, according to the Chebyshev's theorem.\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331246 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=331246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A random sample of 50 gas stations in cook County, Illinois, result in a mean price per gallon of $1.60 and a standard deviation of $0.07. <BR>\n" );
document.write( "a) determine the percentage of gas stations that have prices between $1.46 and $1.74, according to the Empirical Rule.<BR>\n" );
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document.write( "1.46-1.60 = -0.14 = -2*0.07 or 2 standard deviations below the mean.<BR>\n" );
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document.write( "1.74-1.60 =  +0.14 = +2*0.07 or 2 standard deviations above the mean.<BR>\n" );
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document.write( "P(1.46 < x < 1.74) = P(-2 < z < 2) = 0.9545 = 95.45%\r<BR>\n" );
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document.write( "b) Determine the percentage of gas stations that have prices between $1.46 and $1.74, according to the Chebyshev's theorem.<BR>\n" );
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document.write( "Percentage within 2 standard deviations of the mean<BR>\n" );
document.write( "= (1-(1/2)^2) = 0.75 = 75%<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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