document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167442>Question 1167442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Scores on a standardized exam are known to follow a normal distribution with standard deviation σ = 14. A researcher randomly selects 85 students and computes their average score. He reports that the mean score is 73.5, with a margin of error of 1.640.\r<BR>\n" );
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document.write( "How confident are you that the mean score for all students taking the exam is in the interval (71.86, 75.14)?\r<BR>\n" );
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document.write( "Confidence = <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 #792038 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792038\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The half-interval is 1.64<BR>\n" );
document.write( "this equals z*sigma/sqrt(n) or z*14/sqrt(85)<BR>\n" );
document.write( "so z=1.64*sqrt(85)/14=1.08 which is at the 86th percentile for z<BR>\n" );
document.write( "this would be 28% counting both sides or a CI of 72%.\r<BR>\n" );
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