4 A particular product is made from human blood given by donors. The product is stored in bags. The production process is such that, on average, \(5 \%\) of bags are faulty. Each bag is carefully tested before use.

1. 12 bags are selected at random.
   (A) Find the probability that exactly one bag is faulty.
   (B) Find the probability that at least two bags are faulty.
   (C) Find the expected number of faulty bags in the sample.
2. A random sample of \(n\) bags is selected. The production manager wishes there to be a probability of one third or less of finding any faulty bags in the sample. Find the maximum possible value of \(n\), showing your working clearly.
3. A scientist believes that a new production process will reduce the proportion of faulty bags. A random sample of 60 bags made using the new process is checked and one bag is found to be faulty. Write down suitable hypotheses and carry out a hypothesis test at the \(10 \%\) level to determine whether there is evidence to suggest that the scientist is correct.