Assume that the weights of the empty soda bottles of a well-known brand have a normally distributed weight of mean 0.4 kg and standard deviation 0.01 kg. The weight of the liquid that is deposited in the bottles has a normal distribution of mean 0.7 kg and standard deviation 0.05 kg. The weights of the empty boxes where the bottles are placed have a normal distribution of mean 2 kg and standard deviation 0.05 kg. If each box contains 12 bottles filled with such soda;

a) Calculate the standard deviation of the weight of a box containing 12 full bottles.