7. Julia is a quality monitoring officer at a NESCO's production unit which produces metal parts for engineering and construction industries. Over the past year her records show that 25% of a certain type of nuts produced at this production unit was found to be defect.

a. Give two reasons why a binomial distribution may be a suitable model for the number of defect nuts in a pack of 20.

b. Find the probability that a randomly selected pack of 20 nuts from this unit contains no defect nuts at all.

c. Find the mean and variance of the number of defect nuts in a pack of 20.