document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=438120>Question 438120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x has a normal distribution with a mean 15 and standard deviation 3, describe <BR>\n" );
document.write( "                    _<BR>\n" );
document.write( "the distribution of x values for sample size n, where n=4, n=16, and n =100. How <BR>\n" );
document.write( "       _ <BR>\n" );
document.write( "do the x distributions compare for the various sample sizes?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #303041 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=303041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If x has a normal distribution with a mean 15 and standard deviation 3, describe the distribution of x values for sample size n, where n=4, n=16, and n =100. How do the x distributions compare for the various sample sizes?<BR>\n" );
document.write( "----<BR>\n" );
document.write( "The mean of the sample means of any size = the mean of the population.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "The std of the sample means for samples of size n = s/sqrt(n) where<BR>\n" );
document.write( "s is the std of the population.<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "mean for all your distributions is 15<BR>\n" );
document.write( "---<BR>\n" );
document.write( "std for samples of size 4 is 3/sqrt(4) = 3/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "std of samples of size 16 is 3/sqrt(16) = 3/4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "std of samples of size 100 = 3/sqrt(100) = 3/10<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Notice: As the samples size gets larger the spread of the<BR>\n" );
document.write( "distribution gets smaller, or tighter.<BR>\n" );
document.write( "=======================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "===========<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );