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[answered] A manufacturer of computer memory chips produces chips in l


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A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone wrong in the manufacturing process, at most 7 chips each lot would be defective, but if something does go wrong, there could be far more defective chips. If something goes wrong with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip in every lot, so they want to make the decision of whether or not to discard a given lot on the basis of the number of defective chips in a simple random sample. They decide they can afford to test 100 chips from each lot. You are hired as their statistician.

4. (Continues previous problem.) To have a chance of at most 1% of discarding a lot given that the lot is good, the test should reject if the number of defectives in the sample of size 100 is greater than or equal to
5.In that case, the chance of rejecting the lot if it really has 40 defective chips is (Q17)

7. Continues previous problem.) The smallest number of defectives in the lot for which this test has at least a 99% chance of correctly detecting that the lot was bad is

(Continues previous problem.) Suppose that whether or not a lot is good is random, that the long-run fraction of lots that are good is 95%, and that whether each lot is good is independent of whether any other lot or lots are good. Assume that the sample drawn from a lot is independent of whether the lot is good or bad. To simplify the problem even more, assume that good lots contain exactly 7 defective chips, and that bad lots contain exactly 40 defective chips.

8.(Continues previous problem.) The number of lots the manufacturer has to produce to get one good lot that is not rejected by the test has a (Q20) distribution, with parameters
10.(Continues previous problem.) With this test and this mix of good and bad lots, among the lots that pass the test, the long-run fraction of lots that are actually bad is



A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone

 

wrong in the manufacturing process, at most 7 chips each lot would be defective, but if

 

something does go wrong, there could be far more defective chips. If something goes wrong

 

with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip

 

in every lot, so they want to make the decision of whether or not to discard a given lot on the

 

basis of the number of defective chips in a simple random sample. They decide they can afford

 

to test 100 chips from each lot. You are hired as their statistician.

 

4. (Continues previous problem.) To have a chance of at most 1% of discarding a lot given that

 

the lot is good, the test should reject if the number of defectives in the sample of size 100 is

 

greater than or equal to

 

5.In that case, the chance of rejecting the lot if it really has 40 defective chips is (Q17)

 

7. Continues previous problem.) The smallest number of defectives in the lot for which this test

 

has at least a 99% chance of correctly detecting that the lot was bad is

 

(Continues previous problem.) Suppose that whether or not a lot is good is random, that the

 

long-run fraction of lots that are good is 95%, and that whether each lot is good is independent

 

of whether any other lot or lots are good. Assume that the sample drawn from a lot is

 

independent of whether the lot is good or bad. To simplify the problem even more, assume that

 

good lots contain exactly 7 defective chips, and that bad lots contain exactly 40 defective chips.

 

8.(Continues previous problem.) The number of lots the manufacturer has to produce to get one

 

good lot that is not rejected by the test has a (Q20) distribution, with parameters

 

10.(Continues previous problem.) With this test and this mix of good and bad lots, among the

 

lots that pass the test, the long-run fraction of lots that are actually bad is

 


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