document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=728181>Question 728181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have an extra credit sheet, 25 problems similar to these two. Can someone help with an explanation to solve both? Appreciation is unlimited.\r<BR>\n" );
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document.write( "Use the empirical, otherwise known as the 68 - 95 - 99.7 rule.\r<BR>\n" );
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document.write( "1) Distribution is normal. Mean is 10, Standard Deviation is 2, find the percentage of values in the distribution: BELOW 10\r<BR>\n" );
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document.write( "2) Mean is 12, Standard Deviation is 3, find percentage of values in the distribution: ABOVE 18. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #445356 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=445356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "68 percent is within 1 standard deviation of the mean, and 95 percent is within 2 standard deviations of the mean.  Normal distribution means that half of the data is above the mean and half below.\r<BR>\n" );
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document.write( "So for problem 2, if the mean is 12 and the sd is 3, then 18 is exactly 2 standard deviations above the mean.  We know that 95 percent of the data is within 2 standard deviations of the mean, so half of 95 percent, namely 47.5% is within 2 sd below the mean and the other 47.5% is within 2 sd above the mean.  So, adding it all up, 50% is below the mean, then 47.5 is 2 sd above the mean.  Hence 97.5% of the data is less than or equal to 18.  Therefore 1 - 0.975 = 0.025 or 2.5% is greater than or equal to 18.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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