document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464210>Question 464210</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A college requires applicants to have an ACT score in the top 12% of all test scores.  The ACT scores are normally distributed, with a mean of 21.5 and a standard deviation of 4.7.\r<BR>\n" );
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document.write( "	i)	type of distribution: _sampling distributions of mean______________\r<BR>\n" );
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document.write( "	ii)	find the mean: __21.5 points________ and standard deviation: ____4.7 points______\r<BR>\n" );
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document.write( "	iii)	find the following:<BR>\n" );
document.write( "		a.	Find the lowest test score that a student could get and still meet the college’s requirement.\r<BR>\n" );
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document.write( "b.	If 1300 students are randomly selected, how many would be expected to have a test score that would meet the college’s requirement?\r<BR>\n" );
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document.write( "c.	How does the answer to part (a) change if the college decided to accept the top 15% of all test scores?<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 #318831 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=318831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A college requires applicants to have an ACT score in the top 12% of all test scores. The ACT scores are normally distributed, with a mean of 21.5 and a standard deviation of 4.7. <BR>\n" );
document.write( "i) type of distribution: _sampling distributions of mean______________ <BR>\n" );
document.write( "ii) find the mean: __21.5 points________ and standard deviation: ____4.7 points______ <BR>\n" );
document.write( "iii) find the following:<BR>\n" );
document.write( "a. Find the lowest test score that a student could get and still meet the college’s requirement.<BR>\n" );
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document.write( "Find the z-score with a right tail of 12%: invNorm(0.88) = 1.1758<BR>\n" );
document.write( "score = 1.1758*4.7+21.5 = 27.0224<BR>\n" );
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document.write( "b. If 1300 students are randomly selected, how many would be expected to have a test score that would meet the college’s requirement?<BR>\n" );
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document.write( "0.12*1300 = 156<BR>\n" );
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document.write( "c. How does the answer to part (a) change if the college decided to accept the top 15% of all test scores?<BR>\n" );
document.write( "Find the z-value with a left tail of 0.85: invNorm(0.85) = 1.0364<BR>\n" );
document.write( "score = 1.0364*4.7+21.5 = 26.3712<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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