document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176064>Question 176064</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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131178 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=131178\">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( "General Formula: P(x = r) = 5Cr*0.65^r*0.35^(5-r)<BR>\n" );
document.write( "Eg: P(x=3) = 5C3*0.65^3*0.35^2 = 10*0.2746*0.1225 = 0.3364...<BR>\n" );
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document.write( "b) Make a histogram for the r probability distribution.<BR>\n" );
document.write( "I'll let you do that.<BR>\n" );
document.write( "What is the expected number of Republicans who will win office in the coming election?<BR>\n" );
document.write( "E(x) = 0*P(0)+1*P(1)+2*P(2)+3*P(3)+...<BR>\n" );
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document.write( "d) What is the standard deviation of r?<BR>\n" );
document.write( "It's binomial so it's sqrt(npq) = sqrt(5*0.65*0.35) = 1.0665...<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );