A warehouse makes nuts and bolts on two independent machines. The internal diameter of the nuts is normally distributed with mean 0.4cm and the external diameter of the bolts is normally distributed with mean 0.42cm. They both have same variance which is determined by rate of production which corresponds to a standard deviation 0.01cm. A third machine fits the parts together provided the diameter of the nut is strictly greater than that of the bolt, other wise it rejects both.

(a) Find the probability a pair is rejected.

(b) If successive pairs of nut and bolt are produced independently, find the probability that in 20 pairs at least 1 is rejected.

(c) What is the largest value of standard deviation, that would achieve a reduction in the probability that a pair would be rejected to 0.01.

Was struggling with this topic but after working through examples have gotten much better, however not sure how to do this at all. Any help would be greatly appreciated.