**Suppose the true mean and standard deviation are unknown. **

**Create and interpret an X-Bar Chart based on the standard deviation.**

** (Be sure to include your chart!) (NOTE: If there are multiple violations, be sure to state ALL of them!)5. (5 pts) **

Suppose the true mean and standard deviation are unknown. Create and interpret an X-Bar Chart based on the sample range. (Be sure to include your chart!) (NOTE: If there are multiple violations, be surety state ALL of them!)6. (4 pts) Suppose the true mean and standard deviation are unknown. Create and interpret an S Chart.

**(Be sure to include your chart!) (NOTE: If there are multiple violations, be sure to state ALL of them!)7. (4 pts) **

Suppose the true mean and standard deviation are unknown. Create and interpret an R Chart. (Be sure to include your chart!) (NOTE: If there are multiple violations, be sure to state ALL of them!)8. Consider Time2.

Assuming that the true mean and the true standard deviation are unknown, complete the following for an Individuals

(I) Chart.(i) (4 pts)

** Find the following:**

(a) centerline,

(b) 1-sigma limits,

(c) 2-sigma limits and

(d) 3-sigma limits.(ii) (3 pts)

Draw and label the centerline and the 1-, 2-, 3-sigma limits on your Individuals

(I) Chart or attach your computer-generated chart.(iii) (3 pts)

Does the process appear to be in control with respect to the mean? Justify your answer.(NOTE: If there are multiple violations, be sure to state ALL of them!)9. Consider Time2. Assuming that the true mean and the true standard deviation are unknown, complete the following for a Moving Range(MR) Chart.(i) (2 pts)

**Find the following: **

(a) centerline and

(b) 3-sigma limits.(ii) (2 pts)

Draw and label the centerline and the 3-sigma limits on your MR Chart or attach your computer-generated chart.(iii) (3 pts) Does the process appear to be in control with respect to the variation? Justify your answer.(NOTE: If there are multiple violations, be sure to state ALL of them!)10. A bakery is supposed to produce cookies whose average weight after baking is 31 grams.

**To meet quality requirements, it has been decided that specification limits be set at 31.5 ± 1.5 grams.**

(i) If the weight of the cookies is normally distributed with a mean of 31 grams ml and a standard deviation of 0.8 grams, determine the fraction of nonconforming cookie weights. (4 pts)

(ii) If 10,000 cookies are produced using this process, approximately how many cookies will be nonconforming?(2 pts)

(iii) Calculate the process-capability ratio of the process. (3 pts)(iv) Interpret the process-capability ratio found in part (iii). (2 pts)