Question $1.$ A machine is newly installed in a factory to fill bags of flour. The standard weight of

each bag of flour is $2000g\text{'}$s$.$ The installing company operates the machine for one day in order

to test and five samples of the output from the machine are recorded every hour. The average

results for each of the five samples are as follows: $1996,2090,2010,2008,1835,1820,2180,$

$2118$ grams. The specification limits are $+-2\mathrm{.}5\%$ of the target value. The installers completed the

installation based on the above measurements. Assume the variance for the production line $({}^2)$

is $100g.$

$1$a$.$ What is the capability index of this process $($Cp$)?$

$0\mathrm{.}5pt$

$1$b$.$ Is the company capable of producing within the customer's specification limits: $?$

and wh:

$0\mathrm{.}5pt$

Question $2.$ A machine at a Cereal manufacturing company fills boxes with bran flakes cereal.

The target weight for the filled boxes is $24$ ounces. The company would like to use appropriate

control charts to monitor the performance of the machine. To develop the charts, the company

decides to sample and weigh five boxes of cereal each day $($at $8$:$00$ and $11$:$00$ a$.$m$.$ and $2$:$00,$

$5$:$00,$ and $8$:$00$ p$.$m$.)$ for $20$ consecutive days. The data are summarized in the printout below.

Case summaries:

a$.$ Limited to first $100$ cases.

Here are some summary statistics that may help you in answering the below questions

$x$ bar bar mean of MEANWT