Help solving a business and finance word problem please

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joannamartinez

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Feb 19, 2010
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I cannot get this problem. Please advise. 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?Thank you.
 
Julio examines 120 bottles during each hour of his shift.

If 1/50th of any sample is defective, he stops production.

The exercise asks about how many bottles is 1/50th of a sample?

They include the word "about" because this ratio is not a whole number.
 
Could you please simplify it more for me? I am beginning to understand but still not fully. Thank you.
 
joannamartinez said:
I cannot get this problem. Please advise. 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?Thank you.
Click to expand...
We could help better if you showed your work - that might give us the clues we need to interpret the question!

There are a lot of things unsaid or confusing in the statement of the problem. I have tried to fill in the missing details in my own mind - I arrive at a problem that can be treated, but there is no guarantee it is THE problem you are supposed to deal with!

Suppose the "1/50" refers to the population distribution. The null hypothesis might be
H0: the defect rate is less than 2%

Then we take a sample of size 120. Consider a binomial distribution with n=120 and p=0.02. Use what you know about the mean and standard deviation of of the binomial distribution to find the equivalent normal distribution.

Next, consider whether we are being proactive about shutting down the line in case of possible difficulty, OR are we as managers trying to keep production up even if there is a chance of faulty product. That tells you which tail of the normal distribution to use. A nominal critical value might be 95% - but there are still two interpretations. Do you shut down if there is a 5% chance of being bad, OR do you keep running so long as there is a 5% chance of not being bad?

What more do you know about the problem that you haven't told us?
 
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