document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138735>Question 1138735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Repeated random samples of size 36 are drawn from a population (X) with a mean<BR>\n" );
document.write( "µ = 10 and a standard deviation σ = 3. Each sample is used to compute a sample<BR>\n" );
document.write( "mean X bar = ∑X / n .<BR>\n" );
document.write( "(a) What is the mean of these sample means, i.e., what is the value of µ xbar ?\r<BR>\n" );
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document.write( "(b) What is the standard deviation of these sample means, i.e., what is the value of<BR>\n" );
document.write( "σ xbar ? <BR>\n" );
document.write( "(c) What is the shape of the distribution of these sample means? Why? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756554 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)  The mean of the sample means is the mean of the population which is 10<BR>\n" );
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document.write( "(b)  The standard deviation of the samples = 3/square root(36) = 3/6 = 1/2<BR>\n" );
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document.write( "(c)  Normal distribution since all the samples are greater than 30<BR>\n" );
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