Q1. The Marlin Company produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are

	Bottle
Sample	1	2	3	4
1	0.604	0.612	0.588	0.600
2	0.597	0.601	0.607	0.603
3	0.581	0.570	0.585	0.592
4	0.620	0.605	0.595	0.588
5	0.590	0.614	0.608	0.604
6	0.585	0.583	0.617	0.579

a. Assume that only these six samples are sufficient, and use the data to determine regression

b. Suppose that the specification for the bottle neck diameter is 0.600 0.050 in. If the population standard deviation is 0.012 in., and the firm is seeking “4-sigma” quality performance, is the process capable of producing the bottle?

c. If the s.d.=0.012” was not known to you, how would you answer Part (b)?

d. Following Part-B, What percentage of the bottles are expected to fall outside of the required specifications and likely be rejected by the customer?

Q2. Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped. Management is concerned about whether the filling process for tubes of caulking is in statistical control. The process should be centered on 8 ounces per tube. Several samples of eight tubes were taken, each tube was weighed, and the weights in the Table below were obtained.

1. Assume that only six samples are sufficient and develop the 3-sigma control charts and comment on your findings. (No need to plot them).
2. If a major customer requests that the caulking volume per tube must be at 8 +/- 0.2 ounces. Is this process capable of producing less than 2700 defects per million tubes?

Ounces of Caulking per Tube
Tube Number
Sample	1	2	3	4	5	6	7	8
1	7.98	8.34	8.02	7.94	8.44	7.68	7.81	8.11
2	8.33	8.22	8.08	8.51	8.41	8.28	8.09	8.16
3	7.89	7.77	7.91	8.04	8.00	7.89	7.93	8.09
4	8.24	8.18	7.83	8.05	7.90	8.16	7.97	8.07
5	7.87	8.13	7.92	7.99	8.10	7.81	8.14	7.88
6	8.13	8.14	8.11	8.13	8.14	8.12	8.13	8.14

Q3. Management at Webster in the previous problem is now concerned as to whether caulking tubes are being properly capped. If a significant proportion of the tubes are not being sealed, Webster is placing its customers in a messy situation. Tubes are packaged in large boxes of 144. Several boxes are inspected and the following numbers of leaking tubes are found:

Sample	Tubes	Sample	Tubes	Sample	Tubes
1	3	8	6	15	5
2	5	9	4	16	0
3	3	10	9	17	2
4	4	11	2	18	6
5	2	12	6	19	2
6	4	13	5	20	1
7	2	14	1	Total	72

Use the appropriate control charts(s) to assess whether the capping process is in statistical control, with a Type-I error of 1%.

Q4: Analyze the “FCB Loan” Case provided in a separate document and attached data files.