58% of u.s. adults have very little confidence in newspapers. you randomly select 10 u.s. adults. find the…

Answer:

(b) $P(x\geq6)=0.638$

Explanation:

Step1: Recall binomial probability formula

$P(x = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $n = 10$, $p=0.58$, $1-p = 0.42$, and $C(n,k)=\frac{n!}{k!(n - k)!}$

Step2: Calculate $P(x\geq6)$

$P(x\geq6)=P(x = 6)+P(x = 7)+P(x = 8)+P(x = 9)+P(x = 10)$ $P(x = 6)=C(10,6)\times(0.58)^{6}\times(0.42)^{4}=\frac{10!}{6!(10 - 6)!}\times(0.58)^{6}\times(0.42)^{4}=210\times0.0388\times0.0311\approx0.252$ $P(x = 7)=C(10,7)\times(0.58)^{7}\times(0.42)^{3}=\frac{10!}{7!(10 - 7)!}\times(0.58)^{7}\times(0.42)^{3}=120\times0.0225\times0.0741\approx0.201$ $P(x = 8)=C(10,8)\times(0.58)^{8}\times(0.42)^{2}=\frac{10!}{8!(10 - 8)!}\times(0.58)^{8}\times(0.42)^{2}=45\times0.0131\times0.1764\approx0.104$ $P(x = 9)=C(10,9)\times(0.58)^{9}\times(0.42)^{1}=\frac{10!}{9!(10 - 9)!}\times(0.58)^{9}\times(0.42)^{1}=10\times0.0076\times0.42\approx0.032$ $P(x = 10)=C(10,10)\times(0.58)^{10}\times(0.42)^{0}=1\times0.0045\times1 = 0.0045$ $P(x\geq6)=0.252+0.201+0.104+0.032+0.0045 = 0.638$