a. To find the z-score for a height of 64 inches: 
- The formula for the z-score is \(z = \frac { X - \mu } { \sigma } \). 
- Here, \(X = 64\) inches (the height), \(\mu = 64\) inches (the mean), and \(\sigma = 3\) inches (the standard deviation). 
- Plug in the values: 
  \(z = \frac { 64 - 64} { 3} = \frac { 0} { 3} = 0\)
- Therefore, the z-score for a height of 64 inches is 0.

b. To find the height of a woman with a z-score of 1: 
  - Use the formula for converting a z-score back to the original value: \(X = \mu + z \cdot \sigma \). 
  - Here, \(\mu = 64\) inches, \(z = 1\), and \(\sigma = 3\) inches. 
  - Plug in the values: 
   \(X = 64 + 1 \cdot 3 = 64 + 3 = 67\)
  - Therefore, the height of a woman with a z-score of 1 is 67 inches.

Supplemental Knowledge: 

A z-score, also known as a standard score, measures how many standard deviations an element is from the mean of the data set. The formula to calculate a z-score is:

\(z = \frac { ( X - \mu ) } { \sigma } \)

where \(X\) is the value in question, \(\mu \) is the mean, and \(\sigma \) is the standard deviation.

Practical Insights:

Understanding z-scores can be of tremendous assistance in many real-life settings. For instance, standardised testing uses them to compare scores against an average and determine if one student performed above or below average.

Quality control processes in manufacturing industries often use z-scores as part of quality management to ascertain whether measurements for an item fall within acceptable parameters - this helps maintain consistency and ensure quality production processes.

Finance provides another practical use for z-scores. Z-scores can help evaluate investment return risk by comparing them against historical averages.

For students and professionals who want to master statistical concepts like z-scores and their applications, UpStudy offers specialized tools and resources designed to enhance your learning experience. Our Statistics and Probability calculator can help you explore more complex problems involving z-scores and other statistical measures with ease.