document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=415757>Question 415757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Geological engineers are very important people and sometimes work closely with civil <BR>\n" );
document.write( "engineers. In bridge construction, geological engineers conduct water-level surveys to <BR>\n" );
document.write( "measure how level the concrete slabs are. They usually take these measures at eight <BR>\n" );
document.write( "different spots on the slab. We are interested in the maximum differential between <BR>\n" );
document.write( "these spots. Data was collected for over 2300 concrete slabs.  The maximum <BR>\n" );
document.write( "differential, x, had a mean of µ=0.64 inch and a standard deviation of  = 0.176 inch. <BR>\n" );
document.write( "Consider a sample of n=400 slabs selected from those surveyed and let  &#773; represent the <BR>\n" );
document.write( "mean of the sample. These slabs were selected without replacement from the total of 2300 <BR>\n" );
document.write( "slabs collected.  <BR>\n" );
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document.write( "a. Find E (X) and Var(X)<BR>\n" );
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document.write( "b. Find P(X>.63)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #291419 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=291419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are interested in the maximum differential between <BR>\n" );
document.write( "these spots. Data was collected for over 2300 concrete slabs. The maximum <BR>\n" );
document.write( "differential, x, had a mean of µ=0.64 inch and a standard deviation of = 0.176 inch. <BR>\n" );
document.write( "Consider a sample of n=400 slabs selected from those surveyed and let X-bar represent the <BR>\n" );
document.write( "mean of the sample. These slabs were selected without replacement from the total of 2300 <BR>\n" );
document.write( "slabs collected. \r<BR>\n" );
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document.write( "a. Find E (X-bar) = u = 0.64<BR>\n" );
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document.write( "  Var(X-bar) = [0.176/sqrt(400)]^2 = [0.0310]/400 = 0.00007744<BR>\n" );
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document.write( "b. Find P(X-bar >.63) <BR>\n" );
document.write( "z(0.63) = (0.63-0.64)/[0.176/sqrt(400)] = -1.1364<BR>\n" );
document.write( "P(x-bar > 0.63) = P(z > -1.1364) = 0.8721<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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