A company packs parcels of books. Suppose the weights of hardback books are Normally distributed with mean 1.5 kg and standard deviation 0.5 kg; and the weights of paperback books are Normally distributed with mean 0.8 kg and standard deviation 0.3 kg. Assume the weights are all independent of each other.

(a) (5 points) A parcel has three hardback books and six paperback books. Find the probability that the parcel weights more than 11 kg.

(b) (5 points) Find the probability that three hardback books weigh more than six paperback books.

(c) (5 points) A pallet of n hardback books is to be moved. Let T is the total weight of these n books. Suppose P(T>100)0.01. Find the value of n. [Hint: The solutions to a quadratic equation ax2+bx+c=0 is x=(b(b24ac))/2a ]