The lengths of the rods produced by a company are normally distributed with mean 55.6 mm and standard deviation 1.2 mm.

(a) In a random sample of 400 of these rods, how many would you expect to have length less than 54.8 mm? [4]

(b) Find the probability that a randomly chosen rod produced by this company has a length that is within half a standard deviation of the mean. [3]