document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170771>Question 1170771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ACT scores have a mean of 21.3 and 8 percent of the scores are above 27. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851101 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=851101\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve this problem step-by-step using the properties of the normal distribution.\r<BR>\n" );
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document.write( "**1. Understand the Problem**\r<BR>\n" );
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document.write( "* We are given:<BR>\n" );
document.write( "    * Mean (μ) = 21.3<BR>\n" );
document.write( "    * 8% of scores are above 27.<BR>\n" );
document.write( "    * The distribution is approximately normal.<BR>\n" );
document.write( "* We need to find the standard deviation (σ).\r<BR>\n" );
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document.write( "**2. Convert Percentage to Z-score**\r<BR>\n" );
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document.write( "* If 8% of scores are above 27, then 92% of scores are below 27.<BR>\n" );
document.write( "* We need to find the z-score that corresponds to the 92nd percentile (0.92).\r<BR>\n" );
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document.write( "* Using a z-table or calculator, we find the z-score that corresponds to 0.92 is approximately 1.41.\r<BR>\n" );
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document.write( "**3. Use the Z-score Formula**\r<BR>\n" );
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document.write( "* The z-score formula is:<BR>\n" );
document.write( "    * z = (x - μ) / σ<BR>\n" );
document.write( "    * Where:<BR>\n" );
document.write( "        * z is the z-score<BR>\n" );
document.write( "        * x is the data point (27)<BR>\n" );
document.write( "        * μ is the mean (21.3)<BR>\n" );
document.write( "        * σ is the standard deviation (what we want to find)\r<BR>\n" );
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document.write( "* Plug in the values:<BR>\n" );
document.write( "    * 1.41 = (27 - 21.3) / σ\r<BR>\n" );
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document.write( "**4. Solve for Standard Deviation (σ)**\r<BR>\n" );
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document.write( "* 1.41 = 5.7 / σ<BR>\n" );
document.write( "* σ = 5.7 / 1.41<BR>\n" );
document.write( "* σ ≈ 4.04255\r<BR>\n" );
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document.write( "**5. Round to the Nearest Tenth**\r<BR>\n" );
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document.write( "* σ ≈ 4.0\r<BR>\n" );
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document.write( "**Answer**\r<BR>\n" );
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document.write( "The standard deviation is approximately 4.0.<BR>\n" );
document.write( " </SPAN>\n" );
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