A very large batch of components has arrived at a distributo

A very large batch of components has arrived at a distributor. The distributor decides to randomly select 8 components. If the actual proportion of defectives in the batch is 0.055.
Then what is the expected number of defective items and the variance of the number of defective items in the sample?
Your answers can be rounded to four decimal digit accuracy when entered.

Solution

Let X be the random variable such that

X=1 if one randomly chosen item is defective

X=0 otherwise.

so X~Binomial (n=8,p=.055)

E(X)=np=8*.055=.44

V(X)=np(1-p)=.4158