Question

1. Liv attends “Happy Days” preschool. The preschool ran assessments on the children’s motor skills (such as ability to tie a shoe), social skills (such as sharing and saying “please” and “thank you”), and school readiness (such as knowing ABCs and basic counting). The motor skills test has a class mean of 6 with a standard deviation of 1, the social skills test has a class mean of 10 with a standard deviation of 2, and the school readiness test has a mean of 16 with a standard deviation of 4. Liv’s parents are given a report that indicates that her z score for motor skills is –1.11, for social skills it is 0.25, and for school readiness it is 0.

a. The parents do not know what z scores are. Clearly define for them what a z score measures and the advantages of using z scores compared to raw scores.

b. What does a z score = –1.11 mean? A z score of 0.25? A z score of 0?

c. What are Liv’s raw scores on each test?

2. Ernesto just got back his exam grades in three classes. In biology the class mean was 75 with a standard deviation of 10, and Ernesto scored an 80. In political science Ernesto scored a 76, the class mean was 80, and the standard deviation was 12. In statistics the class mean was 84 with a standard deviation of 8, and Ernesto scored an 88. Use z scores to help Ernesto figure out in which class he is doing the best.

3. Roberto learns that his class grades correspond to a z score of 1.5 in psychology, a z score of 1.5 in music, and a z score of 1.5 in speech. Each class had a different mean. The mean in psychology was 82, the mean in music was 75, and the mean in speech was 90. How could he have the same z score in each class if the means are different? Can you determine his raw score in each class?

Answer 1