Specifications are that a product be $101+-8cm.$ The current process is centered on the specs and has a standard deviation of five $cm.$

a$.$ What is the process capability inciex? Round your intermediate and final answers to $4$ decimal places $($e$.$g$.,0\mathrm{.}12345$ would be rounded as $0\mathrm{.}1235,$ not $0\mathrm{.}1234).$

Process capability index

b$.$ Suppose the process average shifts to $98.$ Calculate the new process capability index. Round your intermediate and final answers to $4$ decimal places $($e$.$g$.,0\mathrm{.}12345$ would be rounded as $0\mathrm{.}1235,$ not $0\mathrm{.}1234).$

New process capability index

c$.$ What is the probability of defective output after the process shift? Round $"$z$"$ values to $2$ decimal places as you do the calculations. Enter the answer probability as a decimal $($so $12\mathrm{.}35\%$ would be entered as $\mathrm{.}1235)$ and round your probabilities for your intermediate and final answers to $4$ decimal places $($so a probability of $0\mathrm{.}12345$ would be entered as $0\mathrm{.}1235,$ not $0\mathrm{.}1234$ or $12\mathrm{.}345\%$ or something else$).$

Probability of defective output