document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168534>Question 1168534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose SAT Writing scores are normally distributed with a mean of 489 and a standard deviation of 112.  A university plans to award scholarships to students whose scores are in the top 4%.  What is the minimum score required for the scholarship?  Round your answer to the nearest whole number, if necessary.\r<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 #851561 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=851561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve this problem step-by-step.\r<BR>\n" );
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document.write( "**1. Understand the Problem**\r<BR>\n" );
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document.write( "* SAT Writing scores are normally distributed.<BR>\n" );
document.write( "* Mean (μ) = 489<BR>\n" );
document.write( "* Standard deviation (σ) = 112<BR>\n" );
document.write( "* We need to find the score that corresponds to the top 4%.\r<BR>\n" );
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document.write( "**2. Find the Z-score**\r<BR>\n" );
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document.write( "* We need to find the z-score that corresponds to the top 4% of the distribution.<BR>\n" );
document.write( "* The top 4% means that 96% of the scores are below this point.<BR>\n" );
document.write( "* We need to find the z-score corresponding to a cumulative probability of 0.96.<BR>\n" );
document.write( "* Using a z-table or calculator, we find that the z-score corresponding to 0.96 is approximately 1.75.\r<BR>\n" );
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document.write( "**3. Convert the Z-score to a Raw Score**\r<BR>\n" );
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document.write( "* We use the formula: X = μ + zσ<BR>\n" );
document.write( "* X = 489 + 1.75 * 112<BR>\n" );
document.write( "* X = 489 + 196<BR>\n" );
document.write( "* X = 685\r<BR>\n" );
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document.write( "**4. Round to the Nearest Whole Number**\r<BR>\n" );
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document.write( "* The minimum score required for the scholarship is 685.\r<BR>\n" );
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document.write( "**Therefore, the minimum score required for the scholarship is 685.**<BR>\n" );
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