In the article “An Investigation of the Ca–CO3–CaF2– K2SiO3–SiO2–Fe Flux System Using the Submerged Arc Welding Process on HSLA-100 and AISI-1018 Steels” (G. Fredrickson, M.S. thesis, Colorado School of Mines, 1992), the carbon equivalent P of a weld metal is defined to be a linear combination of the weight percentages of carbon (C), manganese (Mn), copper (Cu), chromium (Cr), silicon (Si), nickel (Ni), molybdenum (Mo), vanadium (V), and boron (B). The carbon equivalent is given by

Means and standard deviations of the weight percents of these chemicals were estimated from measurements on 45 weld metals produced on HSLA-100 steel base metal. Assume the means and standard deviations (SD) are as given in the following table.

a. Find the mean carbon equivalent of weld metals produced from HSLA-1000 steel base metal.

b. Assuming the weight percents to be independent, find the standard deviation of the carbon equivalent of weld metals produced from HSLA-1000 steel base metal.