Over a period of 12 consecutive production hours, samples of size 50 resulted in the following proportions of defective items:

Proportion Proportion Sample Number Defective Sample Number Defective 1 .04 7 .10 2 .02 8 .10 3 .06 9 .06 4 .08 10 .08 5 .08 11 .04 6 .04 12 .04

a. What are the three-sigma control limits for this process?

b. Do any of the sample points fall outside of the control limits?

c. The company claims a defect rate of 3 percent for these items. Are the observed proportions consistent with a target value of 3 percent defectives? What difficulty would arise if the control limits were based on a target value of 0.03? In view of the company’s claims, what difficulty would arise if the control limits computed in part

(a) were used?