A candy manufacturer is marketing a gift box containing four cream-filled nuggets and five pieces of fudge. The manufacturing process for each candyis designed so that the mean weight of a cream-filled nugget is 3 ounces with a standard deviation of 0.2 ounces and the mean weight of a piece of fudge is 4 ounces with a standard deviation of 0.3 ounces. The boxes have a mean weight of 3 ounces with a standard deviation of 0.1 ounces. Assuming the weights of each candy and the box are independent, what is the standard deviation of the weight?