document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192121>Question 1192121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The table below describes results from random selection of eight live births from eight different sets of parents. The random variable x represents the number of girls among the eight live births. Is 6 a significantly high number of girls out of 8 live births?\r<BR>\n" );
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document.write( "Probability Distribution of Girls in x Live Births<BR>\n" );
document.write( "x P(x)\r<BR>\n" );
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document.write( "0 0.004\r<BR>\n" );
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document.write( "1 0.008\r<BR>\n" );
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document.write( "2 0.104\r<BR>\n" );
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document.write( "3 0.251\r<BR>\n" );
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document.write( "4 0.266\r<BR>\n" );
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document.write( "5 0.251\r<BR>\n" );
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document.write( "6 0.104\r<BR>\n" );
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document.write( "7 0.008\r<BR>\n" );
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document.write( "8 0.004<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 #849086 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=849086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to determine if 6 girls out of 8 live births is significantly high:\r<BR>\n" );
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document.write( "1. **Calculate the Mean (μ):**\r<BR>\n" );
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document.write( "   μ = Σ [x * P(x)] <BR>\n" );
document.write( "   μ = (0 * 0.004) + (1 * 0.008) + (2 * 0.104) + (3 * 0.251) + (4 * 0.266) + (5 * 0.251) + (6 * 0.104) + (7 * 0.008) + (8 * 0.004)<BR>\n" );
document.write( "   μ = 4\r<BR>\n" );
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document.write( "2. **Calculate the Standard Deviation (σ):**\r<BR>\n" );
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document.write( "   σ = sqrt( Σ [(x - μ)² * P(x)] )<BR>\n" );
document.write( "   σ = sqrt( (0-4)² * 0.004 + (1-4)² * 0.008 + (2-4)² * 0.104 + (3-4)² * 0.251 + (4-4)² * 0.266 + (5-4)² * 0.251 + (6-4)² * 0.104 + (7-4)² * 0.008 + (8-4)² * 0.004 )<BR>\n" );
document.write( "   σ ≈ 1.27\r<BR>\n" );
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document.write( "3. **Calculate the Range of Usual Values (using the Range Rule of Thumb):**\r<BR>\n" );
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document.write( "   * Lower Bound: μ - 2σ = 4 - 2 * 1.27 ≈ 1.46<BR>\n" );
document.write( "   * Upper Bound: μ + 2σ = 4 + 2 * 1.27 ≈ 6.54\r<BR>\n" );
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document.write( "4. **Compare the Observed Value:**\r<BR>\n" );
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document.write( "   The observed value is 6 girls.\r<BR>\n" );
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document.write( "5. **Make a Decision:**\r<BR>\n" );
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document.write( "   Since 6 falls within the range of usual values (1.46 to 6.54), it is *not* considered significantly high.\r<BR>\n" );
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document.write( "**Conclusion:**\r<BR>\n" );
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document.write( "6 girls out of 8 live births is within the expected range based on the given probability distribution. Therefore, it is not considered a significantly high number.<BR>\n" );
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