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**Sari****Guest**

Julio works as a quality control expert in a beverage factory. The assembly line that he monitors produces about 20,000 bottles in a 24 hour period. Julio samples about 120 bottles an hour and rejects the line if he finds more than 1/50 of the sample to be defective. About how many defective bottles should Julio allow before rejecting the entire line?

I need to know how you got to the answer. Thanks

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Assuming they work poor Julio all day, he will sample 120 x 24 = 2880 bottles in one day. 1/50 of this is 2880 ÷ 50 = 57.6 bottles, so he would reject the line if 58 or more of the bottle were defective.

Why did the vector cross the road?

It wanted to be normal.

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**Sari****Guest**

A friend of mine said 400. Because you divide 20,000 from 50. Why is this wrong so I can tell them?

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Because you are only interested in the bottles that Julio samples. Of the 20,000 bottles produced every day, Julio only samples 2,880 of them. He assumes that if over 1/50 of his sample is faulty then over 1/50 of all the bottles will be faulty and so he rejects the line. In his sample, 1/50 of the bottles is 57.6, so the lowest whole number that is too high is 58 and so he must reject the line if he gets 58 defective bottles or more.

Why did the vector cross the road?

It wanted to be normal.

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**Sari****Guest**

That's where they went wrong then. They were counting the ENTIRE production line, but we were only interested in Julio's amount.

Thanks! I'm glad I found this site. You were a great help!

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