Which of the following statements describes the Z-score's role in quality control?

Which of the following statements describes the Z-score's role in quality control?

• A. It measures the magnitude of the difference in raw units.
• B. It expresses how many standard deviations the result is from the mean.
• C. It predicts future results.
• D. It represents the probability of a result.

Answer: (B)

In quality control, the Z-score is used to standardize how far a measurement is from the process mean, measured in units of the data’s own variability. It expresses the deviation in standard deviation terms, so you can see not just that a result is off, but how far off it is relative to the typical spread of outcomes. This standardization is powerful because it makes results comparable across different tests or metrics that may have different scales or units. A Z-score is unitless, since it’s a ratio of deviation to standard deviation, which lets you apply common decision rules—like flagging results that lie far from the mean. It doesn’t by itself predict future results, and it isn’t a probability, though you can translate a Z-score into a probability under the normal model if you need to assess how unusual a value is.

In quality control, the Z-score is used to standardize how far a measurement is from the process mean, measured in units of the data’s own variability. It expresses the deviation in standard deviation terms, so you can see not just that a result is off, but how far off it is relative to the typical spread of outcomes. This standardization is powerful because it makes results comparable across different tests or metrics that may have different scales or units. A Z-score is unitless, since it’s a ratio of deviation to standard deviation, which lets you apply common decision rules—like flagging results that lie far from the mean. It doesn’t by itself predict future results, and it isn’t a probability, though you can translate a Z-score into a probability under the normal model if you need to assess how unusual a value is.