4. (a) State two conditions under which a random variable can be modelled by a binomial distribution. In the production of a certain electronic component it is found that \(10 \%\) are defective.
The component is produced in batches of 20 .
(b) Write down a suitable model for the distribution of defective components in a batch. Find the probability that a batch contains
(c) no defective components,
(d) more than 6 defective components.
(e) Find the mean and the variance of the defective components in a batch. A supplier buys 100 components. The supplier will receive a refund if there are more than 15 defective components.
(f) Using a suitable approximation, find the probability that the supplier will receive a refund.