document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164665>Question 1164665</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain school in Southern Africa has a total of 400 learners. The IQ scores of all these learners has a standard deviation of 69 and is normally distributed. A sample of 50 of these students had a average IQ score of 174.5. Construct a 98% confidence interval for the true average IQ score of all the learners at this college. Interpret this interval, that is explain in simple English (suitable for publication in a local news paper) what the interval you have constructed above represents. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789220 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=789220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> half-interval is z(0.99)*sigma/sqrt(n)<BR>\n" );
document.write( "=2.328*69/sqrt(50)<BR>\n" );
document.write( "=22.72<BR>\n" );
document.write( "so the interval is (151.8, 197.2)\r<BR>\n" );
document.write( "\n" );
document.write( "We don't know the true mean, but we are very confident, 98% confident, that it lies in the interval we have chosen. Another way of stating this is if we took 100 samples of 50 from this group, 98 of them would have a mean in this interval.  </SPAN>\n" );
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