3. (a) Write down two conditions needed to approximate the binomial distribution by the Poisson distribution. A machine which manufactures bolts is known to produce \(3 \%\) defective bolts. The machine breaks down and a new machine is installed. A random sample of 200 bolts is taken from those produced by the new machine and 12 bolts were defective.
(b) Using a suitable approximation, test at the \(5 \%\) level of significance whether or not the proportion of defective bolts is higher with the new machine than with the old machine. State your hypotheses clearly.