The thickness, Pcm, of a randomly chosen paperback book may be regarded as an observation from a normal distribution with mean 2.0 and variance 0.730. The thickness, H cm, of a randomly chosen hardback book may be regarded as an observation from a normal distribution with mean 4.9 and variance 1.920.

(a) Determine the probability that the combined thickness of four randomly chosen paperbacks is greater than the combined thickness of two randomly chosen hardbacks.

(b) By considering X-2P-H, or otherwise, determine the probability that a randomly chosen paperback is less than half as thick as a randomly chosen hardback.

(c) Determine the probability that a randomly chosen collection of 16 paperbacks and 8 hardbacks will have a combined thickness of less than 70 cm. (Give three decimal places in your answers.) (C)