document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191332>Question 1191332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The distribution of the weights of a sample of 1,400 cargo containers is symmetric and bell-shaped\r<BR>\n" );
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document.write( "According to the Empirical Rule, what percent of the weights will lie between  X⎯⎯⎯−2s  and  X⎯⎯⎯+2s   ?\r<BR>\n" );
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document.write( "According to the Empirical Rule, what percent of the weights will lie between  X⎯⎯⎯  and  X⎯⎯⎯+2s  ? \r<BR>\n" );
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document.write( "According to the Empirical Rule, what percent of the weights will lie below  X⎯⎯⎯−2s  ?\r<BR>\n" );
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document.write( "i need to see steps  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849225 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how the Empirical Rule applies to this situation:\r<BR>\n" );
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document.write( "* **Empirical Rule:** The Empirical Rule (also known as the 68-95-99.7 Rule) applies to distributions that are symmetric and bell-shaped (approximately normal). It states that:\r<BR>\n" );
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document.write( "    * Approximately 68% of the data falls within 1 standard deviation of the mean (between X̄ - s and X̄ + s).<BR>\n" );
document.write( "    * Approximately 95% of the data falls within 2 standard deviations of the mean (between X̄ - 2s and X̄ + 2s).<BR>\n" );
document.write( "    * Approximately 99.7% of the data falls within 3 standard deviations of the mean (between X̄ - 3s and X̄ + 3s).\r<BR>\n" );
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document.write( "* **Between X̄ - 2s and X̄ + 2s:**  According to the Empirical Rule, approximately **95%** of the weights will lie between X̄ - 2s and X̄ + 2s.\r<BR>\n" );
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document.write( "* **Between X̄ and X̄ + 2s:** Since the distribution is symmetric, half of the 95% will lie between the mean and 2 standard deviations above the mean. Therefore, approximately 95%/2 = **47.5%** of the weights will lie between X̄ and X̄ + 2s.\r<BR>\n" );
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document.write( "* **Below X̄ - 2s:** Since 95% of the data is between X̄ - 2s and X̄ + 2s, the remaining 5% is outside this range. Because the distribution is symmetric, half of this 5% (2.5%) will be below X̄ - 2s, and the other half (2.5%) will be above X̄ + 2s.  Therefore, approximately **2.5%** of the weights will lie below X̄ - 2s.<BR>\n" );
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