Help ASAP please Problem 4. In order to decide if a large quantity of supplier b

Question

Help ASAP please Problem 4. In order to decide if a large quantity of supplier bolts 10,000 in quantity] should be qualified to be accepted and used for mass production in a mission critical ground vehicle. A quality engineering manager decides to take a random sample of 20 bolts from the whole batch of supplier bolts, and (i) accept the whole batch if no more than 2 defectives are found; (i) reject the whole batch if more than 5 defectives are found; (ii) take an additional sample of 30 bolts if there are 3 to 5 defectives in the first sample of 20 bolts. Historical data show that 99.98% of bolts are defective free for any given bolt. Assess the probabilities of the above three decision scenarios, i.e., the probability of accept, reject, or resampling, respectively. [15 points

Explanation / Answer

n=20 ; p=0.9998 and = 0.0002

1) P( Accept) = 20C0 * 0.9998^20 +20C1* 0.9998^19*0.0002+20C2*0.9998^18*0.0002^2=1 * 0.9998^20 +20* 0.9998^19*0.0002+190*0.9998^18*0.0002^2=0.999999991

P( Resample) =20C3 * 0.9998^17 *0.0002^3+20C4* 0.9998^16*0.0002^4+20C5*0.9998^15*0.0002^5

P( Reject) = 1-P( accept)-P(resample)

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