document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200840>Question 1200840</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer knows that their items have a normally distributed length, with a mean of 14.3 inches, and standard deviation of 1.7 inches.\r<BR>\n" );
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document.write( "If 12 items are chosen at random, what is the probability that their mean length is less than 14.2 inches?\r<BR>\n" );
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document.write( "Enter your answers as numbers accurate to 4 decimal places.<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 #835985 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=835985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 14.3<BR>\n" );
document.write( "sandard deviation is 1.7<BR>\n" );
document.write( "sample size is 12.<BR>\n" );
document.write( "standard error is 1.7 / sqrt(12) = .4907477288.<BR>\n" );
document.write( "probability that their mean length is less than 14.2 would be .4193 using the online calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = _blank\">https://davidmlane.com/hyperstat/z_table.html</a><BR>\n" );
document.write( "the probability is .4192663762 using the ti-84 plus scientific calculator.<BR>\n" );
document.write( "here's what the results look like using the online calculator.\r<BR>\n" );
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document.write( "the key is that you have to use the standard error, rather than the standard deviation, because you are looking for the mean of a sample of size greater than 1.<BR>\n" );
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