Problem $6$:

The US Treasury is assessing its process capability for minting quarters. With regard to weight, the specification width is $0\mathrm{.}006$ grams. The process is centered at the specification mean of $5\mathrm{.}27$ grams with an upper control limit of $5\mathrm{.}272$ grams and a lower control limit of $5\mathrm{.}268$ grams. What are:

a The upper specification limit$?$

b The lower specification limit$?$

c The process width?

d The process capability index?