Question

A developmental psychologist was interested in how long it would take a particular 7-year-old child to complete three different aptitude tests as compared with 7-year-olds in the general population. The child's time for reading was 31 minutes (population: M = 29, SD = 4). For math, it was 26 minutes (population: M = 32, SD = 2). For science, it was 40 minutes (population: M = 31, SD = 4).Calculate the child's z- scores for each of the aptitude tests. 

Answer 1

Given,

The time for the reading is 31 minutes.

The mean for the reading is 29.

The standard deviation for the reading is 4.

The time for the math is 26 minutes.

The mean for the math is 32.

The standard deviation for the math is 2.

The time for the science is 40 minutes.

The mean for the science is 31.

The standard deviation for the science is 4.

The expression for z score is,

$\begin{gathered} z=\frac{X-\mu}{\sigma} \\ \text{Here,} \\ \mu=\text{ mean} \\ \sigma=\text{ standard deviation} \end{gathered}$

The z score for reading is,

$\begin{gathered} z=\frac{31-29}{4} \\ z=\frac{2}{4} \\ z=0.5 \end{gathered}$

The z score for math is,

$\begin{gathered} z=\frac{26-32}{2} \\ z=\frac{-6}{2} \\ z=-3 \end{gathered}$

The z score for science is,

$\begin{gathered} z=\frac{40-31}{4} \\ z=\frac{9}{4} \\ z=2.25 \end{gathered}$

Hence, the z score of reading is 0.5, math is -3 and science is 2.25.