document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=596202>Question 596202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that 13% of the voters in a state intend to vote for a certain candidate. What is the probability that a survey polling nine people reveals that three or fewer intend to vote for that candidate? (Round your answer to 4 decimal places.)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377592 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=377592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the binomial probability distribution\r<BR>\n" );
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document.write( "P(X = 0) = (9 ncr 0)*(0.13)^(0)*(1-0.13)^(9-0) <BR>\n" );
document.write( "P(X = 0) = (9 ncr 0)*(0.13)^(0)*(0.87)^(9-0) <BR>\n" );
document.write( "P(X = 0) = (1)*(0.13)^(0)*(0.87)^9 <BR>\n" );
document.write( "P(X = 0) = (1)*(1)*(0.285544154243029527) <BR>\n" );
document.write( "P(X = 0) = 0.285544154243029527\r<BR>\n" );
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document.write( "P(X = 1) = (9 ncr 1)*(0.13)^(1)*(1-0.13)^(9-1) <BR>\n" );
document.write( "P(X = 1) = (9 ncr 1)*(0.13)^(1)*(0.87)^(9-1) <BR>\n" );
document.write( "P(X = 1) = (9)*(0.13)^(1)*(0.87)^8 <BR>\n" );
document.write( "P(X = 1) = (9)*(0.13)*(0.3282116715437121) <BR>\n" );
document.write( "P(X = 1) = 0.384007655706143157\r<BR>\n" );
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document.write( "P(X = 2) = (9 ncr 2)*(0.13)^(2)*(1-0.13)^(9-2) <BR>\n" );
document.write( "P(X = 2) = (9 ncr 2)*(0.13)^(2)*(0.87)^(9-2) <BR>\n" );
document.write( "P(X = 2) = (36)*(0.13)^(2)*(0.87)^7 <BR>\n" );
document.write( "P(X = 2) = (36)*(0.0169)*(0.37725479487783) <BR>\n" );
document.write( "P(X = 2) = 0.229521817203671772\r<BR>\n" );
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document.write( "P(X = 3) = (9 ncr 3)*(0.13)^(3)*(1-0.13)^(9-3) <BR>\n" );
document.write( "P(X = 3) = (9 ncr 3)*(0.13)^(3)*(0.87)^(9-3) <BR>\n" );
document.write( "P(X = 3) = (84)*(0.13)^(3)*(0.87)^6 <BR>\n" );
document.write( "P(X = 3) = (84)*(0.002197)*(0.433626201009) <BR>\n" );
document.write( "P(X = 3) = 0.080024848143808932\r<BR>\n" );
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document.write( "In short, \r<BR>\n" );
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document.write( "P(X = 0)= 0.285544154243029527\r<BR>\n" );
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document.write( "P(X = 1)= 0.384007655706143157\r<BR>\n" );
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document.write( "P(X = 2)= 0.229521817203671772\r<BR>\n" );
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document.write( "P(X = 3)= 0.080024848143808932\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "P(X <= 3) = P(X = 0)+P(X = 1)+P(X = 2)+P(X = 3) <BR>\n" );
document.write( "P(X <= 3) = 0.285544154243029527 + 0.384007655706143157 +0.229521817203671772 + 0.080024848143808932 <BR>\n" );
document.write( "P(X <= 3) = 0.979098475296653388\r<BR>\n" );
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document.write( "Answer: \r<BR>\n" );
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document.write( "P(X <= 3) = 0.979098475296653388\r<BR>\n" );
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document.write( "Round this to four places to get P(X <= 3) = 0.9791\r<BR>\n" );
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document.write( "So the the probability that a survey polling nine people reveals that three or fewer intend to vote for that candidate is <font color=\"red\">0.9791</font> </SPAN>\n" );
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