1. Create a Pareto chart for the following mistakes made in grading an exam. Cause Frequency Incorrect Sum 35 Question marked wrong was right 3 Question marked right was wrong 4 Partial Credit not consistent 58 2. Construct a cause-and-effect diagram for why students arrive to class late. Include at least three reasons for each of the Ms. 3. The upper and lower limits for diving ring diameters made by John's Swimming Co. are 40 and 39 cm., respectively. John took 11 samples with the following average diameters (39, 39.1, 39.2, 39.3, 39.4, 39.5 39.6, 39.7, 39.8, 39.9, 40). Is the process in control? 4. A manager wants to build 3-sigma x-bar control limits for a process. The target value for the mean of the process is 10 units, and the standard deviation of the process is 6. If samples of size 9 are to be taken, what will be the upper and lower control limits, respectively? A) -8 and 28 B) 16 and 4 C) 12 and 8 D) 4 and 16 E) 8 and 12 5. A manager wishes to build a 3-sigma range chart for a process. The sample size is five, the mean of sample means is 16.01, and the average range is 5.3. From Table S6.1, the appropriate value of D3 is 0, and D4 is 2.115. What are the UCL and LCL, respectively, for this range chart? A) 33.9 and 11.2 B) 33.9 and 0 C) 11.2 and 0 D) 6.3 and 0 E) 31.91 and 0.11 6. How are common causes and assignable causes different? 7. An operator trainee is attempting to monitor a filling process that has an overall average of 705 cc. The average range is 17 cc. If you use a sample size of 6, what are the upper and lower control limits for the x-bar chart and R-chart? 8. The defect rate for a product has historically been about 1.6%. What are the upper and lower control chart limits for a p-chart, if you wish to use a sample size of 100 and 3-sigma limits? 9. The specification for a plastic liner for concrete highway projects calls for a thickness of 6.0 mm 0.1 mm. The standard deviation of the process is estimated to be 0.02 mm. What are the upper and lower specification limits for this product? The process is known to operate at a mean thickness of 6.03 mm. What is the Cp and Cpk for this process? About what percent of all units of this liner will meet specifications? 10. A local business owner is considering adding another employee to his staff in an effort to increase the number of hours that the store is open per day. If the employee will cost the owner $4,000 per month and the store takes in $50/hour in revenue with variable costs of $15/hour, how many hours must the new employee work for the owner to break even? 11. A firm is considering adding a second secretary to answer phone calls and make appointments. The cost of the secretary will be $10/hour and she will work 200 hours each month. If each new client adds $400 of profit to the firm, how many clients must the secretary arrange for the firm to break even? 12. Fabricators, Inc. wants to increase capacity by adding a new machine. The fixed costs for machine A are $90,000, and its variable cost is $15 per unit. The revenue is $21 per unit. What is the break-even point for machine A? A) $90,000 dollars B) 90,000 units C) $15,000 dollars D) 15,000 units E) 4,286 units 13. A work system has five stations that have process times of 5, 9, 4, 9, and 8. What is the throughput time of the system? A) 4 B) 9 C) 18 D) 35 E) 7 14. A work system has five stations that have process times of 5, 9, 4, 9, and 8. What is the bottleneck time? A) 4 B) 9 C) 18 D) 35