document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161983>Question 1161983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The true proportion of residents at small barangay that favored the genuine opposition senatorial candidates is 85%. What is the probability that at least 75% of the 60 residents favored the genuine opposition? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785709 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=785709\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> can do with binomial, since very little remaining probability. This is pdf<BR>\n" );
document.write( "p(44)=0.0077<BR>\n" );
document.write( "p(43)=0.0035<BR>\n" );
document.write( "p(42)=0.0015<BR>\n" );
document.write( "p(41)=0.0006<BR>\n" );
document.write( "P(40)=0.0002<BR>\n" );
document.write( "cdf is1- binomcdf (60,.85,44) since we want 44 and everything less.<BR>\n" );
document.write( "That is 0.9864 probability, the exact value\r<BR>\n" );
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document.write( "Normal approximation<BR>\n" );
document.write( "The expected value is 51 (60*0.85)<BR>\n" );
document.write( "the variance is np (1-p)=51(0.15)=7.65<BR>\n" );
document.write( "sd is sqrt (V)=2.766<BR>\n" );
document.write( "z>(44.5-51)/2.766=-2.35<BR>\n" );
document.write( "probability is 0.9906 of z>=-2.36, a decent estimate\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );