Final answer:
The z-score for a population value of 16 is -2.25, indicating it is 2.25 standard deviations below the mean. The z-score for a population value of 31 is 1.5, showing it is 1.5 standard deviations above the mean.
Step-by-step explanation:
To calculate the z-score for a population value, we use the formula:
Z = (X - μ) / σ
This formula helps us to determine how many standard deviations a particular value (X) is from the mean (μ) of a population.
a. For a population value of 16:
- Z = (16 - 25) / 4
- Z = -9 / 4
- Z = -2.25
The z-score for a population value of 16 is -2.25, which means it is 2.25 standard deviations below the mean.
b. For a population value of 31:
- Z = (31 - 25) / 4
- Z = 6 / 4
- Z = 1.5
The z-score for a population value of 31 is 1.5, which means it is 1.5 standard deviations above the mean.