document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129662>Question 129662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Long-term history has shown that 65% of all elected offices in a rural county have been won by Republican candidates.  This year there are 5 offices up for public election in the county  Let r be the number of public offices won by Republicans.<BR>\n" );
document.write( "	a)  Find P(r) for r=0,1,2,3,4, and 5<BR>\n" );
document.write( "	b)  Make a histogram for the r probability distribution.<BR>\n" );
document.write( "	c)  What is the expected number of Republicans who will win office in the coming election?<BR>\n" );
document.write( "	d)  What is the standard deviation of r?<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 #94657 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=94657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Long-term history has shown that 65% of all elected offices in a rural county have been won by Republican candidates. This year there are 5 offices up for public election in the county Let r be the number of public offices won by Republicans.<BR>\n" );
document.write( "a) Find P(r) for r=0,1,2,3,4, and 5<BR>\n" );
document.write( "P(1) = 0.65<BR>\n" );
document.write( "P(2) = 5C2(0.65)(0.35)^2 =0.1811...<BR>\n" );
document.write( "P(3) = 5C3(0.65)^2(0.35)=0.3364...<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "b) Make a histogram for the r probability distribution.<BR>\n" );
document.write( "c) What is the expected number of Republicans who will win office in the coming election?<BR>\n" );
document.write( "Random variable values are........1.....2........3..........4.........5..<BR>\n" );
document.write( "Associated probabilities are.....0.65..0.181....0.3364....0.3123...0.116<BR>\n" );
document.write( "To find the expected value ADD the PRODUCTS of each value and its probability.<BR>\n" );
document.write( "The answer I get using a TI calculator is E(x)= 3<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "d) What is the standard deviation of r?<BR>\n" );
document.write( "You have the x-values; you have the P(x) values<BR>\n" );
document.write( "The formula for the standard deviation is sqrt[[Ex^2*P(x)]-mu^2]]<BR>\n" );
document.write( "or you could use the following:<BR>\n" );
document.write( "std = sqrt[E(x-u)^2*P(x)]<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "The answer I get using a TI calculator is std = 0.184478...\r<BR>\n" );
document.write( "\n" );
document.write( "---------<BR>\n" );
document.write( "Note: I typed E where there should be a summation sign.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );