document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206822>Question 1206822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Random samples of size 53 are drawn from a population with mean 104.3 and standard deviation 21.8. Find the mean and the standard deviation of the sample mean. Round to four decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844485 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given the population mean and the population standard deviation, .....\r<BR>\n" );
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document.write( "the mean of the distribution of sample means is equal to the population mean.\r<BR>\n" );
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document.write( "the standard deviation of the distribution of sample means is equal to the population standard deviation divided by the square root of the sample size.\r<BR>\n" );
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document.write( "in this problem,...\r<BR>\n" );
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document.write( "mean of distribution of sample means = 104.3.\r<BR>\n" );
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document.write( "standard deviation of distribution of sample means = 21.8 / sqrt(53) = 2.9945 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "note that the standard deviation of sample means is also called standard error.\r<BR>\n" );
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document.write( "here is a reference on the central limit theorem which is the theory behind the meaning of the distribution of sample means.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.scribbr.com/statistics/central-limit-theorem/#:~:text=The%20central%20limit%20theorem%20states,population%20isn't%20normally%20distributed.\" target = \"_blank\">https://www.scribbr.com/statistics/central-limit-theorem/#:~:text=The%20central%20limit%20theorem%20states,population%20isn't%20normally%20distributed.</a>\r<BR>\n" );
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document.write( "there are many references on the web for the central limit theorem.<BR>\n" );
document.write( "if this one doesn't satisfy you, select another, and another, until you find one that you can understand clearly.\r<BR>\n" );
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document.write( "this one, i found to be pretty good and fairly easily explained.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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