Consolidated Corp. is a manufacturer that produces metal parts. Recently, it signed a contract to supply metal plates to an air conditioning manufacturer. The specifications require the length to be between 14.95 cm and 15.05 cm. With the current production process, Consolidated Corp. manages to produce plates whose length is, on average, equal to 15 cm; however, a closer inspection reveals some variability in the process, with the length of the plate being normally distributed with standard deviation equal to 0.015 cm.

[15 points] What is the capability index (score) of Consolidated Corp.?

[15 points] What is the minimum standard deviation allowed for the process to

meet the rigorous six-sigma standards?