Question

numver 7 please

Answer 1

7:

Let X is a random variable shows the number of components failed. Here X has binomial distribution with parameters as follow:

n = 11,p=0.6

(a)

The probability that 8 component will fail is

$P(X=8)=\binom{11}{8}(0.6)^{8}(1-0.6)^{11-8}=0.1774$

(b)

The mean is

$\mu=np=11\cdot 0.6=6.6$

The standard deviation is

$\sigma=\sqrt{np(1-p)}=\sqrt{11\cdot 0.6\cdot 0.4}=1.6248$

(c)

Something wrong in this part. Probability that 8 component fail out of 11 is less than 0.45 as calculated in part a.