Question 1043351: 30 percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five.
Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 30 percent of households say they would feel secure if they had $50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings.
Find the probability that the number that say they would feel secure is
(a) exactly five:: p(x = 5) = 8C5*0.3^5*0.7^3 = binompdf(8,0.3,5) = 0.0467
(b) more than five::P(6<=x<=8) = 1 - binomcdf(8,0.3,5) = 0.0113
(c) at most five::P(0<=x<=5) = binomcdf(8,0.3,5) = 0.9887
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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 5: 8C5(0.3)^5(0.7)^3=66*0.000833=0.055 (rounded at end)
6:8C6(0.3)^6(0.7)^2=0.010
7:=8(0.3)^7)(0.7)=0.001
8:0.3^8=0.00007
Greater than 5, the last three: 0.011
At most 5 is everything else, the complement of greater than 5, and that is 0.989.
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