Answer
a) $p(X\geq 1)\approx 1$
b)$p(X\geq 3)\approx 0.9999$
c) the mean, $=12.244$
the std. $=2.179$
Work Step by Step
$p(X=x)=\frac{20!}{x!(20−x)!}(0.6122)^{x}(0.3878)^{20−x},x=0,1,...,20$
a) $p(X\geq 1)=1-p(x=0)=1-\frac{20!}{0!(20)!}(0.6122)^{0}(0.3878)^{20}\approx 1$
b)$p(X\geq 3)=1-p(x\lt 3)=1-[p(x=0)+p(x=1)+p(x=2)] \approx 0.9999$
c) the mean, $E(x)=n.p=20(0.6122)=12.244$
the std. $= \sqrt {v(x)}=\sqrt {n.p.(1-p)}=\sqrt {20(0.6122)(0.3878)}=2.179$
