document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160843>Question 1160843</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume a normal distribution with known population variance. Calculate the lower<BR>\n" );
document.write( "confidence limit (LCL) and upper confidence limit (UCL) for each of the following.<BR>\n" );
document.write( "a. 𝑥̅ = 50; n = 64; 𝜎 = 40; α = 0.05<BR>\n" );
document.write( "b. 𝑥̅ = 85; n = 225; 𝜎2 = 400; α = 0.01<BR>\n" );
document.write( "c. 𝑥̅ = 510; n = 485; 𝜎 = 50; α = 0.10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784244 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=784244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> half-interval is z*sigma/sqrt(n), and this is added and subtracted to and from the mean to get the interval limits.\r<BR>\n" );
document.write( "\n" );
document.write( "half-interval for a is z(0.975)*40/sqrt(64)=9.8<BR>\n" );
document.write( "(40.2, 59.8)\r<BR>\n" );
document.write( "\n" );
document.write( "half-interval for b is z(0.995)*20/sqrt (225).  Variance is sigma^2 so have to take the square root of 400 for sigma.<BR>\n" );
document.write( "=2.576*20/15=3.43<BR>\n" );
document.write( "(81.57, 88.43)\r<BR>\n" );
document.write( "\n" );
document.write( "half-interval for c is z(0.95)*50/sqrt(485)<BR>\n" );
document.write( "=1.645*50/sqrt (485)=3.73<BR>\n" );
document.write( "(506.27, 513.73) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );