The maker of grandfather clock needs to be careful about the weights of the swinging pendulums, which is essential to the time-keeping precision. It is desirable for 99.9% of the pendulum to have the weight of 2.20 lbs with tolerance of 0.0004lbs

a)If the process is in statistical control, centered and normally distributed, what is the value of standard deviation that would be required to to meet the criteria of Cp to be at 1.25

b)If the maker of clock finds a pendulum supplier who is willing to meet the criteria of standard deviation in part a, but deviates the average weight of pendulum to 2.2003 lbs in his production but maintains the same tolerance that maker requires. What will be the value of Cp and Cpk for this supplier?

c)The supplier has promised to have long term process performance Pp to be at 1.33 in 6 months. What will be the value of standard deviation if the supplier is still producing the weight of the pendulum at 2.2003 lbs? Is this acceptable? What should the supplier do first before promising Pp of 1.33 at the weight of 2.2003 lbs?