Probability: Is the manager telling the truth?

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The discussion centers on evaluating the manager's claim that 99% of products are unflawed, based on a sample of 50 products where 2 were found to be flawed. A calculation suggests a probability of approximately 7.5% for this outcome if the manager's claim is true, leading to the conclusion that the manager lied. However, it is argued that this probability does not definitively prove dishonesty, as the sample size may not be representative and could result from random chance. More testing is necessary to draw a stronger conclusion about the manager's truthfulness. Ultimately, the evidence is insufficient to confirm that the manager is lying.
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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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