document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201663>Question 1201663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please solve this equation: <BR>\n" );
document.write( "The mean of a normal probability distribution is 300; the standard deviation is 16.\r<BR>\n" );
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document.write( "a. About 68% of the observations lie between what two values?<BR>\n" );
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document.write( "b. About 95% of the observations lie between what two values?\r<BR>\n" );
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document.write( "c. Practically all of the observations lie between what two values?<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 #836136 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=836136\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answers:<ol type=\"a\"><li><font color=red>284 and 316</font></li><li><font color=red>268 and 332</font></li><li><font color=red>252 and 348</font></li></ol>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "We use the Empirical Rule.<BR>\n" );
document.write( "Some textbooks call it the 68-95-99.7 rule but I don't think it's as catchy of a name.\r<BR>\n" );
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document.write( "The rule has 3 properties:<ul><li>roughly 68% of the normal distribution is within 1 standard deviation of the mean.</li><li>roughly 95% of the normal distribution is within 2 standard deviations of the mean.</li><li>roughly 99.7% of the normal distribution is within 3 standard deviations of the mean.</li></ul><BR>\n" );
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document.write( "For part (a), the work shown would be something like this<BR>\n" );
document.write( "mu - 1*sigma = 300 - 1*16 = 284<BR>\n" );
document.write( "mu + 1*sigma = 300 + 1*16 = 316<BR>\n" );
document.write( "Roughly 68% of the observations are between 284 and 316.\r<BR>\n" );
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document.write( "For part (b), we have<BR>\n" );
document.write( "mu - 2*sigma = 300 - 2*16 = 268<BR>\n" );
document.write( "mu + 2*sigma = 300 + 2*16 = 332<BR>\n" );
document.write( "Roughly 95% of the observations are between 268 and 332.\r<BR>\n" );
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document.write( "For part (c), the phrasing \"practically all\" means \"practically 100%\" which is close enough to 99.7%<BR>\n" );
document.write( "mu - 3*sigma = 300 - 3*16 = 252<BR>\n" );
document.write( "mu + 3*sigma = 300 + 3*16 = 348<BR>\n" );
document.write( "Roughly 99.7%, aka practically all, of the observations are between 252 and 348.<BR>\n" );
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