Chapter 5, Problem 40PE

A supplier contract calls for a key dimension of a part to be between $\text{1}\text{.96 and 2}\text{.04}$ centimeters. The supplier has determined that the standard deviation of its process, which is normally distributed, is $0.03$ centimeter.

1. If the actual mean of the process is $1.98$, what fraction of parts will meet specifications?
2. If the mean is adjusted to $2.00$, what fraction of parts will meet specifications?
3. How small must the standard deviation be to ensure that no more than $2\%$ of parts are nonconforming, assuming the mean is $2.00$ ?