Answer
a) $p(X=3)\approx 0.2347$
b)$p(X\geq 3)\approx 0.4921$
c) the mean $=2.6$
the std. $= 1.5040$
Work Step by Step
Given that, n=20, p=0.13, this means that
$p(X=x)=\frac{20!}{x!(20−x)!}(0.13)^{x}(0.87)^{20−x},x=0,1,...,20$
a) $p(X=3)=\frac{20!}{3!(17)!}(0.13)^{3}(0.87)^{17}\approx 0.2347$
b)$p(X\geq 3)=1-p(x\lt 3)=1-[p(x=0)+p(x=1)+p(x=2)] \approx 0.4921$
c) the mean, $E(x)=n.p=20(0.13)=2.6$
the std. $= \sqrt {v(x)}=\sqrt {n.p.(1-p)}=\sqrt {20(0.13)(0.87)}=1.5040$
