Question

7) A z-score of 0.5 is at what percentile? a) 25th b) 50th c) 69th d) 84th 8) Abdul obtains a score of 13 on the WAIS-IV Block Design test. If this is the only information that you have, your best est

Answer 1

7) The z-score of 0.5 corresponds roughly to the 69th percentile. Therefore, the correct choice is c) 69th.

Step-by-step explanation:

A z-score represents the number of standard deviations a particular value is from the mean in a normal distribution. The percentile associated with a z-score can be found using a standard normal distribution table or calculator. For a z-score of 0.5, we refer to the standard normal distribution table which indicates that approximately 69.15% of the area under the curve falls below a z-score of 0.5.

To compute percentiles from z-scores, the z-score is essentially the number of standard deviations away from the mean. A z-score of 0 is at the 50th percentile since it's at the mean, and positive z-scores denote values above the mean in a standard normal distribution. Therefore, a z-score of 0.5, being a positive value, lies between the mean and the first standard deviation, roughly placing it around the 69th percentile.

Understanding z-scores and percentiles is vital in analyzing data distribution. In this case, a z-score of 0.5 indicates that the value falls relatively close to the upper end of the distribution, approximately in the 69th percentile, indicating it's higher than about 69% of the data in a standard normal distribution curve. Thus, the correct choice for this question is c) 69th percentile.