Question

How can the empirical rule be restated in terms of z-scores and percentiles?

a. The empirical rule is not applicable to z-scores and percentiles
b. The empirical rule states that all z-scores are equal to percentiles
c. The empirical rule is irrelevant to the concept of z-scores and percentiles
d. The empirical rule is not explicitly stated in terms of z-scores and percentiles

Answer 1

The empirical rule can be restated in terms of z-scores and percentiles as follows: within one standard deviation of the mean (68%), the z-scores range from -1 to +1; within two standard deviations of the mean (95%), the z-scores range from -2 to +2; within three standard deviations of the mean (99.7%), the z-scores range from -3 to +3.

Step-by-step explanation:

The empirical rule can be restated in terms of z-scores and percentiles as follows:

1. Within one standard deviation of the mean (68%), the z-scores range from -1 to +1.
2. Within two standard deviations of the mean (95%), the z-scores range from -2 to +2.
3. Within three standard deviations of the mean (99.7%), the z-scores range from -3 to +3.

These ranges of z-scores correspond to the percentiles of the data distribution, indicating the proportions of values that fall within each range.