Probability: Is the manager telling the truth?

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SUMMARY

The discussion centers on evaluating the truthfulness of a factory manager's claim that 99% of products are unflawed. A sample of 50 products revealed 2 flaws, leading to a calculated probability of approximately 7.54% that the observed result could occur under the manager's claim. However, the consensus is that this probability does not definitively prove the manager's dishonesty, as the sample size may not be representative. Further testing is necessary to draw a more conclusive judgment on the manager's statement.

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Homework Statement



The manager of a factory proclaims 99% of the products manufactured in his factory are unflawed. If we draw 50 products from 5000 products and find 2 of 50 are flawed, then how do we know the manage is telling the truth?

Homework Equations



Nothing special.

The Attempt at a Solution



Answer:

\frac{{5000*0.99 \choose 48} {5000*0.01 \choose 2}}{ {5000 \choose 50}} \approx 0.0754

Manager lied.

Is this correct? Thank you in advance!
 
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You cannot conclude that the manager lied based on this result. You could have been unlucky with the 50 products. A probability of 7.5% is still reasonable and needs more tests before such a strong conclusion can be drawn.
 

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