document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201038>Question 1201038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> No length of a lumber, a machine cuts are normally distributed by a mean of 89 inches and a standard deviation of 0.5 inch part a what is the probability that a randomly selected board cut by the machine has a length greater than 89.12 inches part B hey sample of 41 boards is randomly selected what is the probability that their main length is greater than 89.12 inches </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835290 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the lengths of lumber a machine cuts are normally distributed with a mean of 89 inches and a standard deviation of 0.5 inches.\r<BR>\n" );
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document.write( "part a:<BR>\n" );
document.write( "what is the probability that a randomly selected board cut by the machine has a length greater than 89.12 inches.\r<BR>\n" );
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document.write( "part b:<BR>\n" );
document.write( "what is the probability that a randomly selected sample of 41 boardshas a mean length greater than 89.12 inches.\r<BR>\n" );
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document.write( "answer to part a:<BR>\n" );
document.write( "mean is 89 inches.<BR>\n" );
document.write( "standard deviation is .5 inches.<BR>\n" );
document.write( "probability that the board has a length greater than 89.12 inches is .4052.\r<BR>\n" );
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document.write( "answer to part b:<BR>\n" );
document.write( "mean is 89 inches<BR>\n" );
document.write( "standard deviation is .5<BR>\n" );
document.write( "sample size is 41<BR>\n" );
document.write( "standard error is .5 / sqrt(41) = .0780868809.<BR>\n" );
document.write( "probability that the mean length of the sample will be greater thana 89.12 is .06217731.\r<BR>\n" );
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document.write( "when you are dealing with a sample of one element, use the standard deviation.<BR>\n" );
document.write( "when you are dealing with the mean of a sample of more than 1 element, use the standard error.\r<BR>\n" );
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document.write( "the standard error is equal to the standard deviation divided by the square root of the sample size.\r<BR>\n" );
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document.write( "here's what the results look like on the calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "display from patt a:\r<BR>\n" );
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document.write( "display from part b:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/031702.jpg\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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