The oxygen equivalence number of a weld is a number that can be used to predict properties such as hardness, strength, and ductility. The article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds” (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s–136s) presents several equations for computing the oxygen equivalence number of a weld. One equation, designed to predict the hardness of a weld, is X = O + 2N + (2/3)C, where X is the oxygen equivalence, and O, N, and C are the amounts of oxygen, nitrogen, and carbon, respectively, in weight percent, in the weld. Suppose that for welds of a certain type, μ_O = 0.1668, μ_N = 0.0255, μ_C = 0.0247, σ_O = 0.0340, σ_N = 0.0194, and σ_C = 0.0131.

a. Find μ_X .

b. Suppose the weight percents of O, N, and C are independent. Find σ_X .