At a heat-treating company, iron castings and steel forgings are heat-treated to achieve desired mechanical properties and machinability. One steel forging is annealed to soften the part for each machining. Two lots of this part, made of 1020 steel, are heat-treated in two different furnaces. The specification for this part is 36-66 on the Rockwell G scale. Let X1 and X2 equal the respective hardness measurements for parts selected randomly from furnaces 1 and 2. Assume that the distributions of X1 and X2 are N(47.88,2.19) and N(43.04,14.89), respectively.
(a) Sketch the pdfs of X1 and X2 on the same graph.
(b) Compute P(X1 > X2), assuming independence of X1 and X2.