Question $1[14$ marks$]$

On the Table $1$ below is a typical attribute chart form with information concerning $2-$L soda bottles.

a$)$ Calculate the proportion nonconforming for sub$-$groups $21,22,23,24$ and $25.$ Construct a run chart

$[5$ marks$]$

b$)$ Calculate the trial central line and control limits$.$ Draw these values on the chart.

$[9$ marks$]$

$\backslash$table$[[$Day$,$Sample $($n$),$Numbernonconforming $($np$)],[1,400,43],[2,400,21],[3,400,14],[4,400,20],[5,400,15],[6,400,16],[7,400,8],[8,400,12],[9,400,18],[10,400,4],[11,400,6],[12,400,12],[13,400,5],[14,400,4],[15,400,3],[16,400,8],[17,400,7],[18,400,31],[19,400,8],[20,400,6],[21,400,4],[22,400,7],[23,400,9],[24,400,6],[25,400,10]]$