SOLUTION: 27% of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters wh

Question 1122799: 27% of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least 4, (c) less than eight.
Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
7% of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is::
Binomial Problem with n 12 and p = 0.07
(a) exactly three,
P(x = 3) = 12C3*0.07^3*0.93^9 = binompdf(12,0.07,3) =
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(b) at least 4,
P(4<=x<=12) = 1 - P(0<= x <=3) = 1 - binomcdf(12,0.07,3) = 0.0075
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(c) less than eight.
P(0<= x <= 7) = binomcdf(12,0.07,7) = 0.9999
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Cheers,
Stan H.
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Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
exactly 3: 12C3*0.27^3*0.73^9=0.2549
2: 0.2068
1: 0.1016
0:0.73^12=0.0229
So, at least 4 is 1- the above sum or 0.4138
Less than 8 is <=7 or 0.9953.
This makes sense, since the expected value is 0.27*12=3.24
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