document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167267>Question 1167267</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lengths of lumber a machine cuts are normally distributed with a mean of 105 inches and a standard deviation of 0.3 inch.<BR>\n" );
document.write( "​(a) What is the probability that a randomly selected board cut by the machine has a length greater than 105.13 ​inches?<BR>\n" );
document.write( "​(b) A sample of 37 boards is randomly selected. What is the probability that their mean length is greater than 105.13 ​inches?<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 #791882 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=791882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the first one is z>(105.13-105)/.3 and that is z>0.4333, or probability of 0.3324<BR>\n" );
document.write( "the second one is z>(105.13-105)/.3/sqrt(37) or z>.13*sqrt(37)/.3, or probability of 0.0042<BR>\n" );
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