2. Ten items are to be sampled from a lot of 60. If more than one is defective,

Question

2. Ten items are to be sampled from a lot of 60. If more than one is defective, the lot will be rejected. Assume that there are 10 defective items in the lot. a. What is the probability that the lot will be rejected? (5 points) b. If three different quality control inspectors independently take samples of size 10 from the same lot of 60, what is the probability that at least one of them rejects the lot? (5 points) c. Now, twenty items are to be sampled from a lot of 500, 100 of which are defective. What is the probability that five of the selected items are defective? (5 points

Explanation / Answer

Ans:

Probability of being defective,p=10/60=1/6

a)P(x>1)=1-P(x=0)-P(x=1)

=1-10C0*(1/6)0*(5/6)10-10C1*(1/6)1*(5/6)9

=1-0.1615-0.3230

=0.5155

b)P(y>=1)=1-P(y=0)=1-P(none of them reject)=1-(1-0.5155)3=1-0.48453=1-0.1137=0.8863

c)probabilty of being defcetive=100/500=0.2

P(x=5)=20C5*(0.2)5*(0.8)15=0.1746

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