The size of cakes from The Great British Baking Show have an average weight of 3 pounds with a standard deviation of 0.5 pounds (lb). The size of slices from cakes have an average weight of 0.5 pounds with a standard deviation of 0.15 pounds (lb).

Let X be the weight of a cake after three slices have been removed from it.Determine the standard deviation for X. Include units. Round your answer to at least three decimal places.