Design specifications require that a key dimension on a product measure $105+-14$ units. A process being considered for producing this product has a standard deviation of three units.

a$.$ What can you say $($quantitatively$)$ regarding the process capability? Assume that the process is centered with respect to specifications. $($Round your answer to $4$ decimal places.$)$

Process capability index

b$.$ Suppose the process average shifts to $97.$ Calculate the new process capability. $($Round your answer to $4$ decimal places.$)$

New process capability index

c$.$ What is the probability of defective output after the process shift? $($Use Excel's NORM.S$.$DIST$()$ function to find the correct probability. Round $"z"$ values to $2$ decimal places. Round probabilities to $4$ decimal places $(0.$###$).)$

Probability of defective output