Large and small bottles of water are manufactured in a factory. The volume of water in the large bottles follows a Normal distribution with mean 1.5 litres and standard deviation 0.01. The volume of water in the small bottles follows an independent Normal distribution with mean 0.5 litres and standard deviation 0.008.

(a) (5 points)One large bottle and three small bottles are chosen at random. What is the probability that the volume in the large bottle is greater than the total volume in the three small bottles?

(b) (5 points) Find the distribution of the total volume of 10 large bottles and 3 small bottles.