Question $3$

A bakery is reviewing the packaging process for its cookies. For each box of cookies,

the designed weight is $450$ grams plus or minus $20$ grams. The review monitored $7$

samples where each sample has $5$ observations. The following table summarises the

values of the mean and range for each sample. The overall mean was found to be $454$

and the average range was $14.$

Question $3$a

Due to the negligence of the reviewer, two data points were missing in the table. Based

on the given information, what are the missing numbers in the table?

$(6$ marks$)$

Question $3$b

Comment on whether this process is under control using the $x$ bar chart and $R$ chart.

$(12$ marks$)$

Question $3$c

Determine the process capability index $Cp.$ Is this index alone sufficient to figure out

natural variations from various causes in a process? Why?