The US mint has just installed a new machine for making quarters. One of the critical

measurements of the quarter is its weight. For the first $20$ days of operation, a sample was

taking every hour and weighed. The results are shown in the table below. Using the data in the

table:

a$.$ Based on the calculated upper and lower control limits$.$

b$.$

Calculate $Cp$

and

Cpk$.$

c$.$

Is the process capable?

Is the process centered?

d$.$ The engineered specifications state the weight limits should be between $5\mathrm{.}45$ to $5\mathrm{.}85,$ with a desired

sped of $5\mathrm{.}64$ Given these UCL and LCL$,$ determine the Cp and Cpk Values.

Calculate $Cp$

and

Cpk$.$

Is the process capable?

Is the process centered?

e$.$ Create $x$ bar and $R$ charts

f$.$ What does the $x$ bar and $R$ chart show you about the process?