•Question 3: Lots of 40 are unacceptable, ifthey contain 3 or more defectives. T

Question

•Question 3: Lots of 40 are unacceptable, ifthey contain 3 or more defectives. The quality control procedureis: sampling 5 items at random. If a defective found in thesample, then reject the lot, otherwise accept it. •Q1. What is the probability of accepting a "bad" lotcontaining 3 defectives? •Q2. What is the probability of rejecting it? •Q3. What do you think about utility of this plan? •Question 3: Lots of 40 are unacceptable, ifthey contain 3 or more defectives. The quality control procedureis: sampling 5 items at random. If a defective found in thesample, then reject the lot, otherwise accept it. •Q1. What is the probability of accepting a "bad" lotcontaining 3 defectives? •Q2. What is the probability of rejecting it? •Q3. What do you think about utility of this plan?

Explanation / Answer

Lot size=40;   n=5. Let X be the number ofdefects in the sample. X is binomial with n=5 and p thefraction of defects in a lot. Hence P(X=k)=C(n,k)pk(1-p)n-k      where           C(n,k)=n!/k!(n-k)! Sampling Plan calls for: P(reject lot)=P(X>=1): P(accept lot)=P(X=0) (a)P(X=0 given p=3/40)=(1-p)5=.6672 (b)P(reject)=1-P(accept)=.3228 (c)Not a good plan. High probability of accepting a badlot.

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