document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172473>Question 1172473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Random samples of three are drawn from a population of beetles whose lengths have a normal distribution with mean 2.4 cm and standard deviation 0.36 cm.the mean length is calculated for each sample. <BR>\n" );
document.write( "A-State the distribution of X^- giving the value of its parameters. <BR>\n" );
document.write( "B-find p(X^- >2.5)<BR>\n" );
document.write( "State which of the numerical value above if any depend on the central limit theorem.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797563 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=797563\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample distribution N~(2.4, 0.0432) or mean 2.4 and sd 0.21; the variance is sigma^2/n<BR>\n" );
document.write( "probability X^> 2.5 is z > (2.5-2.4)/0.21 or <BR>\n" );
document.write( "z > 0.476<BR>\n" );
document.write( "which is probability 0.3170.  This comes from the table or from the calculator 2ndVARS2normalcdf(0.476,6) or any number greater than 6.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "So long as the population itself is normal, the sampling distribution of samples with size 3 will also have a normal distribution with the above parameters. </SPAN>\n" );
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