Problem $13-5($Algo$)$

Design specifications require that a key dimension on a product measure $105+-12$ 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.$)$

Answer is complete but not entirely correct.

Process capability index

$0\mathrm{.}6667$

b$.$ Suppose the process average shifts to $98.$ Calculate the new process capability. $($Round your answer to $4$ decimal places.$)$

$$ Answer is complete but not entirely correct.

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 $(0.$###$).)$

$$ Answer is complete but not entirely correct.

Probability of defective output