The life, in years, of a randomly chosen Flashpan car battery is normally distributed with mean 2 and standard deviation 0.4. Show that the probability that a randomly chosen Flashpan battery has a life less than one year is 0.006 21, correct to five places of decimals.

(a) A farmer bays two randomly chosen Flashpan batteries. Find the probability that the batteries each have a life more than one year.

(b) A wholesaler buys 500 randomly chosen Flashpan batteries. Using a suitable approximation, find the probability that at most three have lives each less than one year.

(c) A retailer buys ten randomly chosen Flashpan batteries. Find the probability that at least four have lives each exceeding two years. (C)