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

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(75887) (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...
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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)+...
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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.

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