document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136414>Question 1136414</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe the sampling distribution of P HAT with caret based on large samples of size n -- that ​is, given the​ mean, the standard​ deviation, and the​ (approximate) shape of the distribution of P HAT with caret when large samples of size n are​ (repeatedly) selected from the binomial distribution with a probability of success p. Let q=1-p.\r<BR>\n" );
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document.write( "The mean of the sampling distribution of p HAT is? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754208 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=754208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The mean is np, and with large samples (especially for very small p or q), it is a normal distribution.\r<BR>\n" );
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document.write( "The variance is np(1-p) or npq<BR>\n" );
document.write( "the std dev is sqrt (np(1-p)) or sqrt (npq) </SPAN>\n" );
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