Ross and Sammy, Inc. manufactures Oscar brand of pencils. A random sample of 100 pencils is inspected every day, looking specifically for 4 opportunities for defects in each inspected pencil - lead, wood, eraser, and grip. During a recent day, quality inspector, Denzel, found a total of 8 defects overall in a sample of 100 pencils.

Calculate and report the Defects per Million Opportunities (DPMO), rounded to two places after the decimal, for that sample.

Q2)

The pressure in a household water pipe averages 59 PSI and has a standard deviation of 3 PSI. The lower and upper specifications for this water pressure from Licensing Inspector, Olivia Rodrigo, are 50 PSI and 70 PSI.

2. Calculate and report the Process Capability Ratio (Cp), rounded to two places after the decimal.
4. Calculate and report the Process Capability Index (Cpk), rounded to two places after the decimal.

Q3) The information applies to Q3, Q4,

Patty Pizza shop collects data on the number of errors (i.e., defects) in pizza orders. The errors are not defined beforehand, and can include a wide variety of issues such as incorrect toppings, incorrect address, discount coupon not applied, special seasoning packet missing, etc.... The data provided below noted in samples of 100 orders each taken daily for 10 days. Shop owner, Finneas, has requested your help to generate a Count (c) control chart to track the process.

Day	Errors (Defects)
1	16
2	11
3	10
4	18
5	27
6	17
7	15
8	19
9	15
10	12

Please help Finneas by calculating and reporting, the value for theCenter Line(rounded to thenearestwhole number) of the Count (c) control chart.

Q4)

Ref to data and the answer from q3

Calculate and report the value for the Upper Control Limit (UCL) (rounded to thepreviouswhole number)andthe Lower Control Limit (LCL) (rounded to thenextwhole number) of the Count (c) control chart.

Q5)

Management of the Bobby Golf Pro Shop collects data on the number of dissatisfied customers for their visits using a survey of customers conducted soon after their golf rounds are completed. Customers respond to a single question indicating on a Yes/No scale whether they were satisfied or dissatisfied with their golf rounds. The data provided below gives the number of dissatisfied customers noted in 135 responses each week over 12 weeks. Pro Shop Manager Nile Rodgers, has requested your help in using a control chart to assess the process. Please calculate and report what is the value of theCenter Line (only)for the Proportion (p) control chart. (Nile Rodgers can complete the rest of the calculations for this p chart). Please round your final answer in proportion to 2 places after the decimal.

Week	Number Dissatisfied
1	12
2	9
3	15
4	18
5	12
6	15
7	6
8	27
9	15
10	12
11	9
12	12

Q6)

At the Black Swan Hotel, manager Kai collected extremely precise data in minutes on check-in times using a sample (sub-group) of 6 check-ins per day over a period of 30 days. An excerpt of that data, consisting of the first 5 days of data, are shown below (no Excel file for this question).

	Observations
	1	2	3	4	5	6
Day 1	6.00	4.33	7.33	7.00	6.00	5.00
Day 2	5.75	8.25	2.33	4.25	5.75	7.50
Day 3	7.00	7.75	6.75	6.25	7.00	6.50
Day 4	5.67	8.25	7.25	6.75	6.00	7.50
Day 5	7.00	5.00	4.75	6.25	5.50	6.50

Kai would like your help in identifying what control chart(s) to use.

2. Please identify and report the type of control chart(s) that would be appropriate if only this data is available, and provide a one-sentence justification for the same.
4. Describe in words how you would go about calculating the Center Line(s) for the control chart(s) including what you would need to get from each sample individually and from all samples together.

Please show detailed calculations with formulas so that i can understand the concepts.