Quality Control $-5$

The next $4$ questions refer to the following situation:

In the provided blank, insert the letter that corresponds to the correct answer. For example, if the correct answer is $"$a$)1\mathrm{.}990",$ insert only $"$a$"$ as the correct answer.

A chocolate company manufactures $4$ ounces chocolate bars. Random samples of size five were taken and weighted. Eight hours of observation provided the following data:

Use the above information to answer the following questions $($always round to two decimal places$)$:

I. Determine the lower and upper control limits for the $x-$bar control chart. The letter associated with the correct answer is

a$)2\mathrm{.}93$ and $3\mathrm{.}11$ respectively.

b$)2\mathrm{.}95$ and $2\mathrm{.}09$ respectively.

c$)2\mathrm{.}83$ and $3\mathrm{.}21$ respectively.

d$)2\mathrm{.}80$ and $3\mathrm{.}07$ respectively.

e$)$ None of the above

II$.$ Is the central process in control, explain why? The letter associated with the correct answer is

a$)$ No$,$ because exactly two $x-$bar values fall outside the control interval.

b$)$ No$,$ because exactly three $x-$bar values fall outside the control interval.

c$)$ No$,$ because exactly four $x-$bar values fall outside the control interval.

d$)$ Yes, because all $x-$bar values fall within the control interval.

e$)$ None of the above

III. Determine the lower and upper control limits for the R$-$control chart. The letter associated with the correct answer is

a$)0\mathrm{.}00$ and $0\mathrm{.}32$ respectively.

b$)0\mathrm{.}00$ and $0\mathrm{.}34$ respectively.

c$)0\mathrm{.}02$ and $0\mathrm{.}28$ respectively.

d$)0\mathrm{.}02$ and $0\mathrm{.}30$ respectively.

e$)$ None of the above

IV$.$ Is the variability of the process in control, explain why? The letter associated with the correct answer is

a$)$ Yes, because all $R$ values fall within the control interval.

b$)$ No$,$ because exactly one $R$ value fall outside the control interval.

c$)$ No$,$ because exactly two $R$ values fall outside the control interval.

d$)$ No$,$ because exactly three $R$ values fall outside the control interval

e$)$ None of the above