Final answer:
The correct answer is option b, as a z-score standardizes values from a normal distribution to a standard normal distribution. Additionally, z-scores allow for consistent statistical procedures across different normal distributions and the calculation of probabilities.
Step-by-step explanation:
The correct answer to the question is option b: a z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution. Option c is also correct as it supports the fact that standard z-scores allow for uniform procedures across different normal distributions. The core idea of the z-score is that it measures the number of standard deviations a given value is from the mean of its distribution, transforming it to a standardized score in the standard normal distribution (mean of 0 and standard deviation of 1). This is crucial for comparisons across different datasets and for the calculation of probabilities and areas under the normal curve corresponding to specific values.
Using the z-score formula (z = (x - μ) / σ), where x is the value in the original distribution, μ is the mean, and σ is the standard deviation, any score can be converted to a z-score. This standardization process enables us to use the z-table to find areas under the curve, highlighting the utility of the standard normal distribution in statistical analysis. If we have the z-score, we can then find the corresponding area under the curve, either to the left or right of the score, providing us with the probability of occurrence of scores in that distribution.