The thickness of manufactured metal plates is the variable of interest. Due to many factors, such as slight variations in the metal, different operators, and different machines, the thickness varies and can be considered a normal random variable with mean =20mm and standard deviation =0.04 mm. How much scrap can be expected if the thickness of the metal plates

(a) Has to be at least 19.95 mm

(b) Can be at most 20.10 mm

(c) can differ at most by 0.05mm from the target 20 mm?

(d) How would one have to set the tolerance limits 20-c and 20+c such that one produces at most 5 percent scrap?

(e) Assume that the mean has shifted to 20.10. Calculate the percentage of metal plates that exceed the tolerance limits in part (d).

Please as much CLEAR details as possible