Problem $1.(13$pts$)$

Refer to textbook Chapter $3,$ Problem $3$ on page $126$ for background information and data. But instead of the textbook questions answer the following $5$ questions, show your work to receive credit:

What is the sample size $($n$)?(1$pt$)$

Write down the UCL, CL$,$ and LCL for a $3-$sigma x$-$bar chart $($Please note that: Target mean $()=45$ and R$-$bar $($R $)=6,$ use these numbers for your control chart calculations!$).(4$pts$)$

Now, plot the means $($x $)$ of the five samples $($the sample data is in the table in the textbook problem$)$ on the control chart you created in part $($b$)$ above $($show your work$).$ Then state if the process mean is in control $($Yes$/$No$)?$ Explain why or why not it is in control to receive credit. $(2$pts$)$

Write down the UCL, CL$,$ and LCL for a $3-$sigma R$-$chart $($NOTE: R$-$bar $=6,$ use this number for your control chart calculation!$).(4$pts$)$

Plot the ranges of the five samples $($the sample data that you will plot is in the table in the textbook problem$)$ on the control chart you created in part $($d$)$ above $($show your work$).$ Then state if the variability is in control $($Yes$/$No$)?$ Explain why or why not to receive credit. $(2$pts$)$