What percent of scrap and rework is process now producing

Question

Assignment:

Problem

Assume that the Length (L) is the most important characteristic to the quality of product X. The length is normally distributed variable N_L ~(μ_oσ²₀)= (20 mm, 4 mm²). The specification limits are 20 mm t3 mm. Assuming that if an to, tem exceeds the upper specification limit it can be reworked, and if it is below the lower specification limit it must be scrapped

A. The process is running now at N_L~(μ₁, σ²₀)= (22 mm, 4 mm²). What percent of scrap and rework is the process now producing? Show the drawings.

B. The process is running now at N_L~ (μ₁,σ²₀) = (23 mm, 4 mm²). What percent of scrap and rework is the process now producing? Show the drawings.

c. (Optional) The process is running now at N_L~(μ₀,σ²₁)= (20 mm, 6 mm²). What percent of scrap and rework is or the process now producing? Show the drawings. Note: this is the case when the shift occurs only in the process variance.

No	Leoph	No	Length	No		No	Length	No	Length
					Length
1	9.5	12	9	23	10	34	10	45	10
2	10.98	13	11.71	24	11.04	35	10	46	8.76
3	10.2	14	9.89	25	10.5	38	9.9	47	9.93
4	9	15	10.04	26	10.2	37	10.19	48	10.76
5	9.5	16	10.02	27	10	38	8.52	49	11.23
8	9.5	17	9.75	28	9.84	39	8.07	50	10.42
7	9.6	18	10.03	29	10.22	40	11.82	51	9.04
8	10.31	19	11.34	30	9.74	41	10.02	52	10.09
9	9.38	20	10.2	31	9.8	42	10	53	9.43
10	10.1	21	10.03	32	10	43	10.2	54	9
11	10.54	22	10.03	33	10.2	40	10	55	10