Question 560313: a supplier of components to an industry makes a product which sometimes fails immediately it is used. He control his manufacturing process so that the proportion of faulty products is supposed to be only 5%. Out of 400 supplies in a batch 26 prove to be faulty. Verify the manufacturer's claim. Use 0.05 level of significance
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! in a proportion, the mean is equal to n*p which becomes .05*400 which becomes 20.
this means that the average number of failures for a batch of 400 will be equal to 20.
in a proportion, the standard deviation is equal to sqrt(n*p(1-p)).
for this batch, the standard deviation would be sqrt(400*.05*(.95)) which would be equal to sqrt(19) which would be equal to 4.358898944 which can be rounded to 4.3589
we have a mean of 20 and a standard deviation of 4.3589
at the 95% confidence level, the limits are between 11.455 and 28.545.
this means that a sample batch of data falls within these limits 95% of the time and falls outside these limits 5% of the time.
26 defective for this batch falls within the 95% confidence limits, supporting the manufacturer's claim.
that's what i think, anyway.
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