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Title: Forty Forty percent of households say they would feel secure if they had $50,000 in savings. You ... Post by: Catracho on Jan 8, 2019 Forty
Forty 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. (a) Find the probability that the number that say they would feel secure is exactly five. Title: Re: Forty Forty percent of households say they would feel secure if they had $50,000 in savings. ... Post by: bio_man on Jan 8, 2019 For this you use the binomial distribution formula: \(P\left(r\right)=_nC_r\times \pi ^r\left(1-\pi \right)^{n-r}\), where \(\pi\) is the probability.
45% is equivalent to 0.45 in decimal form. For the probability of exactly 5, you set n = 8, r = 5, \(\pi\) = 0.45, and \(1-\pi =0.55\) \(P\left(5\right)=_{8}C_5\times 0.45^3\left(0.55\right)^{8-5}\) \(P\left(5\right)=_8C_5\times 0.45^3\left(0.55\right)^{8-5}=56\cdot 0.01516=0.849\) For this, find the probabilities of 6, 7 and 8, and add them up. \(P\left(r>5\right)=P\left(6\right)+P\left(7\right)+P\left(8\right)\) \(_8C_6\times 0.45^6\left(0.55\right)^2+_8C_7\times 0.45^7\left(0.55\right)^1+_8C_8\times 0.45^8\left(0.55\right)^0=0.0884\rightarrow 0.088\) 1 minus the answer above. We already found the probabilities of greater than 5, to find at most five means 5 is the maximum. \(P\left(r\le 5\right)=1-P\left(r>5\right)=1-0.08845=0.9115\rightarrow 0.912\) |