Problem $10-21($Algo$)$

Design specifications require that a key dimension on a product measure $110+-13$ 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.

Note: Round your answer to $4$ decimal places.

Process capability index

$1\mathrm{.}0833$

b$.$ Suppose the process average shifts to $98.$ Calculate the new process capability.

Note: Round your answer to $4$ decimal places.

New process capability index

$0\mathrm{.}0833$

c$.$ What is the probability of defective output after the process shift?

Note: Use Excel's NORM.S$.$DIST function to find the correct probability. Round $"$z$"$ values to $2$

decimal places. Round your answer to $4$ decimal places.

Probability of defective output

$0\mathrm{.}4052$