A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results?

Machine $1$ Measirement $17151517$

Machine $2$ Measurement $16251825$

Machine $3$ Measurement $232423221.$ What are the R chart three sigma upper and lower control limits$?$

$2.$ What are the x$-$bar chart three sigma upper and lower control limits$?$

$3.$ For above upper and lower control limits$,$ which machine$($s$),$ if any, appears$)$ to have an out$-$of$-$

control process mean?

$4.$ Studies on a bottle$-$filling machine indicates it fills bottles to a mean of $16$ ounces with a standard deviation of $0\mathrm{.}10$ ounces. What is the process specification, assuming the Cp index of $1?$

$5.$ The specification limit for a product is $8$ cm and $10$ cm$.$ A process that produces the product has a mean of $9\mathrm{.}5$ cm and a standard deviation of $0\mathrm{.}2$ cm$.$ What is the process capability?