document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194048>Question 1194048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A population has a mean of µ = 100 and ơ = 15. Find the mean and standard deviation of the sampling distribution of samples means with sample size n.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = 15<BR>\n" );
document.write( "n= 250<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 #826127 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=826127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Regardless of the value of n, the mean of the sampling distribution is always gong to be mu = 100 in this case.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If n = 15, then we have this standard deviation for the sampling distribution<BR>\n" );
document.write( "sigma/sqrt(n)<BR>\n" );
document.write( "15/sqrt(15)<BR>\n" );
document.write( "3.87298<BR>\n" );
document.write( "which is approximate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If n = 250, then,<BR>\n" );
document.write( "sigma/sqrt(n)<BR>\n" );
document.write( "15/sqrt(250)<BR>\n" );
document.write( "0.94868<BR>\n" );
document.write( "is the approximate standard deviation for the sampling distribution\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As n increases, the standard deviation for the sampling distribution decreases. <BR>\n" );
document.write( "Intuitively it means that as the sample gets larger, we are narrowing in on the population parameter (there's less spread as the data is getting more consistent)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Summary:<BR>\n" );
document.write( "mean = 100 for each case<BR>\n" );
document.write( "standard deviation = 3.87298 approximately when n = 15<BR>\n" );
document.write( "standard deviation = 0.94868 approximately when n = 250<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );