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 c

Question 129662: 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
P(1) = 0.65
P(2) = 5C2(0.65)(0.35)^2 =0.1811...
P(3) = 5C3(0.65)^2(0.35)=0.3364...
etc.
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?
Random variable values are........1.....2........3..........4.........5..
Associated probabilities are.....0.65..0.181....0.3364....0.3123...0.116
To find the expected value ADD the PRODUCTS of each value and its probability.
The answer I get using a TI calculator is E(x)= 3
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d) What is the standard deviation of r?
You have the x-values; you have the P(x) values
The formula for the standard deviation is sqrt[[Ex^2*P(x)]-mu^2]]
or you could use the following:
std = sqrt[E(x-u)^2*P(x)]
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The answer I get using a TI calculator is std = 0.184478...
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Note: I typed E where there should be a summation sign.
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Cheers,
Stan H.

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