document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170403>Question 1170403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the given confidence interval to find the sample mean where the left endpoint is 3.144 and the right endpoint is 3.176. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851208 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the left endpoint of the confidence interval be $L$ and the right endpoint be $R$. We are given $L = 3.144$ and $R = 3.176$.\r<BR>\n" );
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document.write( "The sample mean $\bar{x}$ is the midpoint of the confidence interval. Therefore, we can find the sample mean by averaging the left and right endpoints:<BR>\n" );
document.write( "$$\bar{x} = \frac{L + R}{2}$$\r<BR>\n" );
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document.write( "Substituting the given values, we get:<BR>\n" );
document.write( "$$\bar{x} = \frac{3.144 + 3.176}{2}$$<BR>\n" );
document.write( "$$\bar{x} = \frac{6.320}{2}$$<BR>\n" );
document.write( "$$\bar{x} = 3.160$$\r<BR>\n" );
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document.write( "Thus, the sample mean is $3.160$.\r<BR>\n" );
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document.write( "Final Answer: The final answer is $\boxed{3.16}$<BR>\n" );
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