document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113053>Question 1113053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims that the machine cuts lumber to a mean length of 7 feet &#8203;(84 &#8203;inches) with a standard deviation of 0.7 inch. Assume the lengths are normally distributed. You randomly select 45 boards and find that the mean length is 84.15 inches. Complete parts&#8203; (a) through&#8203; (c).\r<BR>\n" );
document.write( "\n" );
document.write( "&#8203;(a) Assuming the&#8203; seller's claim is&#8203; correct, what is the probability that the mean of the sample is 84.15 inches or&#8203; more?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728102 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=728102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims that the machine cuts lumber to a mean length of 7 feet &#8203;(84 &#8203;inches) with a standard deviation of 0.7 inch. Assume the lengths are normally distributed. You randomly select 45 boards and find that the mean length is 84.15 inches. <BR>\n" );
document.write( "Complete parts&#8203; (a) through&#8203; (c). <BR>\n" );
document.write( "&#8203;(a) Assuming the&#8203; seller's claim is&#8203; correct, what is the probability that the mean of the sample is 84.15 inches or&#8203; more?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "z(84.15) = (84.15-84)/(0.7/sqrt(45) = 1.437<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(u >=84.15) = P(z >= 1.437) = normalcdf(1.437,100) = 0.0753<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "----------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );