# SOLUTION: 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 co

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: 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 co      Log On

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 Question 176064: 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. a) Find P(r) for r=0,1,2,3,4, and 5 b) Make a histogram for the r probability distribution. c) What is the expected number of Republicans who will win office in the coming election? d) What is the standard deviation of r?Answer by stanbon(57219)   (Show Source): You can put this solution on YOUR website!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. a) Find P(r) for r=0,1,2,3,4, and 5 General Formula: P(x = r) = 5Cr*0.65^r*0.35^(5-r) Eg: P(x=3) = 5C3*0.65^3*0.35^2 = 10*0.2746*0.1225 = 0.3364... ----------------------------------------------------------- b) Make a histogram for the r probability distribution. I'll let you do that. What is the expected number of Republicans who will win office in the coming election? E(x) = 0*P(0)+1*P(1)+2*P(2)+3*P(3)+... ---------------------------------------- d) What is the standard deviation of r? It's binomial so it's sqrt(npq) = sqrt(5*0.65*0.35) = 1.0665... Cheers, Stan H. Cheers, Stan H.