Probability and Statistics (Check my answer)

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SUMMARY

The discussion focuses on calculating the percentage of rejected bolts from a batch of 2000, given a mean diameter of 9.711mm and a standard deviation of 0.126mm. The tolerance range provided is 9.73mm to 9.97mm. The initial calculation incorrectly assumes the mean is within the tolerance range, leading to a rejection estimate of approximately 57 bolts. However, participants point out that the mean should be reconsidered, as it does not align with the tolerance limits provided.

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c00ky
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Hi guys, i was given the following problem:

The mean diameter of a batch of bolts is 9.711mm and the standard deviation of the batch is 0.126mm

The tolerance for this batch of components is 9.73mm to 9.97mm.
In a batch of 2000 bolts, determine the following:

a) The percentage of bolts rejected assuming the bolts are normally distributed.

My answer:

(9.97 - 9.73) / 0.126 = 1.90

1.90 Corresponds to: 0.9713

1 - 0.9713 = 0.0287

(Little less than 3% are rejected)

0.0287 x 2000 = 57.4

= 57 rejected out of 2000

Can anybody tell me if I'm right?
 
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No, your first step is not right. But I'm not sure you have written down the problem correctly. If the mean is 9.711, you would expect the tolerated values to go from somewhere below 9.711 to somewhere above it, not from 9.73 to 9.97. Did you mean that the mean is 9.811?
 

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