document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189929>Question 1189929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a population proportion is 0.32 and if the sample size is 100, 45% of the time the sample proportion will be more than what value if you are taking random samples? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822112 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=822112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard error is sqrt(p*(1-p)/n)=sqrt(0.32*0.68/100)=0.0466<BR>\n" );
document.write( "45% of the time greater occurs with a z=+0.1257<BR>\n" );
document.write( "z*SE is margin of error or in this instance the value where 45% are more than the mean of 32 with a sample size of 100. It is 0.0059<BR>\n" );
document.write( "so the proportion is 0.326 and for 100, that would be a mean of 32.6<BR>\n" );
document.write( "-<BR>\n" );
document.write( "can check by approximation<BR>\n" );
document.write( "mean is np=32<BR>\n" );
document.write( "variance is np(1-p)=32*0.68=21.76<BR>\n" );
document.write( "sd is sqrt (V)=4.66<BR>\n" );
document.write( "0.1257 of that sd is 0.59, and add that to the mean and get 32.6 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );