document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137935>Question 1137935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lengths of lumber a machine cuts are normally distributed with a mean of 93 inches and a standard deviation of 0.6 inch.<BR>\n" );
document.write( "​(a) What is the probability that a randomly selected board cut by the machine has a length greater than 93.24 ​inches?<BR>\n" );
document.write( "​(b) A sample of 44 boards is randomly selected. What is the probability that their mean length is greater than 93.24 ​inches? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755873 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=755873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(x-mean)/sd<BR>\n" );
document.write( ">(93.24-93)/0.6=0.4<BR>\n" );
document.write( "probability z>0.4=0.3446\r<BR>\n" );
document.write( "\n" );
document.write( "for the sample, z>(xbar-mu)/sigma/sqrt(n)<BR>\n" );
document.write( "this is 0.24*sqrt(44)/0.6, invert and multiply when dividing<BR>\n" );
document.write( "z>2.65<BR>\n" );
document.write( "probability is 0.0040\r<BR>\n" );
document.write( "\n" );
document.write( "Far less likely 44 boards will deviate by the same amount compared to one. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );