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# An accrediting agency set up a proficiency test for a lab in

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An accrediting agency set up a proficiency test for a lab in [#permalink]

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11 Aug 2003, 10:20
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An accrediting agency set up a proficiency test for a lab in which 20% of the samples were injected with a contaminant. If the lab correctly labelled 80% of the contaminated samples but incorrectly labelled 5% of the uncontaminated samples, then what percent of the samples labelled by the lab as uncontaminated were actaully contaminated ?

(A) 4%
(B) 5%
(c) 10%
(D) 20%
(E) 25%
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Brainless

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11 Aug 2003, 11:17
4 out of 80 labelled uncontaminated are actually contaminated.

(B) 5%
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11 Aug 2003, 15:15
mciatto wrote:
4 out of 80 labelled uncontaminated are actually contaminated.

(B) 5%

Ah!! Is that easy .. It appeared as a hard nut......
Can I get a more detailed explanation ?

Thx!
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Brainless

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11 Aug 2003, 17:53
Brainless wrote:
mciatto wrote:
4 out of 80 labelled uncontaminated are actually contaminated.

(B) 5%

Ah!! Is that easy .. It appeared as a hard nut......
Can I get a more detailed explanation ?

Thx!

I picked #'s, in this case 100 samples.

20 of these are actually contaminated, while 80 are uncontaminated.
If they correctly labelled 80% of the contaminated samples, then that means they labelled 16 out of the 20 correctly, but there are still 4 contaminated ones sitting out there. Now they labelled 5% of the uncomtaminated samples wrong as well, so they marked 4 as being contaminated when they are indeed not. So in the end there are 80 marked uncontaminated, but from the beginning (when they marked only 16 out of the 20 contaminated) there are four of them that are contaminated.
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