document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=234924>Question 234924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> it is assumed that labour productivity of particular members in a factory can be described by a normal distribution with sigma=3.what is probability that a sample mean calculated for 9 randomly chosen workers differs from the population mean by more than 2 units?<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 #173175 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=173175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it is assumed that labour productivity of particular members in a factory can be described by a normal distribution with sigma=3.what is probability that a sample mean calculated for 9 randomly chosen workers differs from the population mean by more than 2 units?<BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "The std of the sample means is 3/sqrt(3).<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Comment: You did not post a mean value for the population<BR>\n" );
document.write( "and I made the mistake of assuming it was 3.  All the<BR>\n" );
document.write( "work I did is based on that assumption.<BR>\n" );
document.write( "Check your problem statement.  Maybe that phrase<BR>\n" );
document.write( "\"more that 2 units\" refers to standard deviation <BR>\n" );
document.write( "units.<BR>\n" );
document.write( "------------------------------------------------------- <BR>\n" );
document.write( "If x-bar differs from the mean by more that 2 units,<BR>\n" );
document.write( "x-bar is less than 1 or x-bar is greater than 5.<BR>\n" );
document.write( "------<BR>\n" );
document.write( "z(1) = (1-3)/sqrt(9) = -2/3<BR>\n" );
document.write( "z(5) = (5-3)/sqrt(9) = 2/3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "P(x-bar < 1)= P(z < -2/3) = 0.2525<BR>\n" );
document.write( "P(x-bar > 4)= P(z > 2/3) = 0.2525<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Ans: 0.2525+0.2525 = 0.5050<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" );