At one stage in the manufacture of an engine a piston of circular cross-section has to fit into a similarly-shaped cylinder. The distributions of diameters of pistons and cylinders are known to be normal with parameters:

• Piston diameters: mean 10.42cm, standard deviation 0.03cm.

• Cylinder diameters: mean 10.52cm, standard deviation 0.04cm.

(a) What is the probability that in 100 pairs, selected independently and at random, every piston will fit?

Any help would be greatly appreciated