document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1024221>Question 1024221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a recent survey, 73% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, a) find the probability that exactly 8 of them favor the building of the police substation. b) less than 3 of them favor the building of the police substation.\r<BR>\n" );
document.write( "\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 #639664 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=639664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Question:<BR>\n" );
document.write( "In a recent survey, 73% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, a) find the probability that exactly 8 of them favor the building of the police substation. b) less than 3 of them favor the building of the police substation.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "Assuming the surveyed 73% still holds, and that the population is large enough such that 14 is a relatively small fraction of the population, and that the 14 subjects are randomly and independently chosen, then we can apply the binomial distribution, with parameters n=14, p=0.73.<BR>\n" );
document.write( " <BR>\n" );
document.write( "(a) 8 in favour out of random sample of 14<BR>\n" );
document.write( "P(X=8;14;0.73)=C(14,8)*0.73^8*(1-0.73)^(14-8)<BR>\n" );
document.write( "=3003*0.08065*0.0003874<BR>\n" );
document.write( "=0.09383\r<BR>\n" );
document.write( "\n" );
document.write( "(b) less than 3 in favour out of 14<BR>\n" );
document.write( "P(0&le;X&le;2; 14, 0.73)<BR>\n" );
document.write( "= P(0)+P(1)+P(2)<BR>\n" );
document.write( "= 1.09419^-08 + 4.141711^-07 + 7.278674^-06<BR>\n" );
document.write( "= 7.703787^(-06)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );