document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=526304>Question 526304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): <BR>\n" );
document.write( "Assume that the population standard deviation on each part of the test is &#963; = 100.\r<BR>\n" );
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document.write( "What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Round your answer to four decimal places.\r<BR>\n" );
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document.write( "What is the probability a random sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test? Round your answer to three decimal places.<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 #348413 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=348413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): <BR>\n" );
document.write( "Assume that the population standard deviation on each part <BR>\n" );
document.write( "of the test is &#963; = 100.<BR>\n" );
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document.write( "What is the probability a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Round your answer to four decimal places.<BR>\n" );
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document.write( "Find the z-values 5% to the right and 5% to the left of z = 0.<BR>\n" );
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document.write( "invNorm(0.45) = -0.1257 <BR>\n" );
document.write( "invNorm(0.55) = +0.1257<BR>\n" );
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document.write( "Find the corresponding raw scores using x = zs+u<BR>\n" );
document.write( "x = -0.1257*100+515 = 502.4339<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = +0.1257*100+515 = 525.5700<BR>\n" );
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document.write( " <BR>\n" );
document.write( "What is the probability a random sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test? Round your answer to three decimal places.<BR>\n" );
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document.write( "I'll do part of this one; you can do the rest.<BR>\n" );
document.write( "5 below 494 = 489<BR>\n" );
document.write( "std for the sample means of size n = 100 is 100/Sqrt(100) = 10<BR>\n" );
document.write( "z(489) = (489-494)/10 = -1/2<BR>\n" );
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document.write( "Similarly the z-score above 494 will be +1/2<BR>\n" );
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document.write( "Then P(489 <= x-bar <= 499) = P(-1/2<= z <=1/2) = 0.3829<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=============\r<BR>\n" );
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