Question

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Formulas for Questions 24-27 Upper control in. UCL= 1 + 20 Lower control it. LCL - P - 20% where p mean traction detective in the sample 2 of normal standard deviations for 99.73%) standard deviation of the sampling distribution /P(1-P) size of each sample

Answer 1

Question 24)

p-bar = Total number of defective/(no of samples*sample size) = 54/(9*70) = 0.085714286

Sp = sqrt((0.085714286*(1-0.085714286))/70) = 0.033459431

UCL = 0.085714286+3*0.033459431 = 0.186092579 = 0.19 (approximately)

LCL = 0.085714286+3*0.033459431 = -0.014664007 = 0 (Adjusted)

So correct answer is 0.19,0

Question 25)

Graph Data

Sample no	Number defective	Fraction defective	center line	LCL	UCL
1	4	0.057	0.0857143	0	0.186093
2	5	0.071	0.0857143	0	0.186093
3	0	0	0.0857143	0	0.186093
4	7	0.1	0.0857143	0	0.186093
5	14	0.2	0.0857143	0	0.186093
6	2	0.029	0.0857143	0	0.186093
7	1	0.014	0.0857143	0	0.186093
8	7	0.1	0.0857143	0	0.186093
9	14	0.2	0.0857143	0	0.186093

p-chart 1 2 3 4 5 6 9 7 LCL 8 UCL - Fraction defective center line -

Correct answer is The percentage defective is out of control

Question 26)

The standard deviation of the sampling distribution is 0.033459431 = 0.0335 (approximately) (Ans)

Question 27)

Correct answer is At least one sample is outside the control limits