Final answer:
The z-score that indicates the value farthest below the mean from the options provided is b) z = -1.50, as it reflects a value that is 1.5 standard deviations below the mean, which is more extreme than the other available z-scores.
Step-by-step explanation:
The question asks which of the following z-scores indicates a value that falls farthest below the mean for the distribution: a) z = -0.50, b) z = -1.50, c) z = +2.00, d) z = +1.25. A z-score represents the number of standard deviations an element 'X' is from the mean of its distribution. A negative z-score indicates that 'X' is less than the mean; the more negative the z-score, the farther below the mean the original score 'X' is located.
To determine which z-score indicates the value farthest below the mean, we look for the most negative value. The choices presented lead to z = -1.50 being the correct answer, as it represents a value that is 1.5 standard deviations below the mean, which is the farthest below the mean relative to the other given options.