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.
What are the p.d.f.s of X1 and X2?
Compute P(X1>X2), assuming independence of X1 and X2.
Thank you for your help!
You compute the z-score corresponding to X3=0 when X3~N(47.88-43.04, 2.19+14.89), (and remember that the second argument here is the variance not the SD). Now look up the z-score in the normal table.Can I get the answer to the second part from the normal distribution table? I looked on the P(Z>z) table to find P(X3>0)=0.5000