NorMetal rods produced by a machine have lengths that are normally distributed. 2% of the rods are rejected as being too short and 5% are rejected as being too long.

a) Given that the least and greatest acceptable lengths of the rods are 6.32 cm and 7.52 cm, calculate the mean and variance of the lengths of the rods.

b) If ten rods are chosen at random from a batch produced by the machine, find the probability that exactly three of them are rejected as being too long.