Design specifications require that a key dimension on a product measure $100+-11$ units. A process being considered for producing this product has a standard deviation of four 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

b$.$ Suppose the process average shifts to $92.$ Calculate the new process capability. $($Round your answer to $4$ decimal places.$)$

New process capability

c$.$ What is the probability of defective output after the process shift? $($Use Excel's NORMSDIST$()$ function to find the correct probability for your computed Zvalue.Round $"z"$ value to $2$ decimal places and final answer to $4$ decimal places.$)$

Probability of defective

output