Bolts are manufactured which are to fit in holes in steel plates. The diameter of the bolts is normally distributed with mean 2.60 cm and standard deviation 0.03 cm. The diameter of the holes is normally distributed with mean of 2.71 cm and standard deviation of 0.04 cm.

(a) Verify that, if a bolt and a hole are selected at random, the probability that the bolt is too large to enter the hole is 0.0139.

(b) The random selection of a bolt and hole is carried out five times. Find the probability that in every case the bolt will be able to enter the hole. (C)