A supplier contract calls for a key dimension of a part to, Basic Statistics

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A supplier contract calls for a key dimension of a part to

Question: A supplier contract calls for a key dimension of a part to be between 1.96 and 2.04 centimeters. The supplier has determined that the standard deviation of its process, which is normally distributed, is 0.04 centimeter.

a. If the actual mean of the process is 1.98, what fraction of parts will meet specifications?

b. If the mean is adjusted to 2.00, what fraction of parts will meet specifications?

c. How small must the standard deviation be to ensure that no more than 2% of parts are nonconforming, assuming the mean is 2.00?

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