Question

b. Find the score (X value) that corresponds to each of the following z-scores. (Again, you should not needa formula or any serious calculations.)

Answer 1

`\begin{gathered} \text{When z=1: }X=48 \\ \text{When z=0.25: }X=42 \\ \text{When z=1.50: }X=52 \\ \text{When z=-0.50: }X=36 \\ \text{When z=-1.25: }X=30 \\ \text{When z=-2.50}X=20 \end{gathered}`

Explanation:

Given a population with:

• Mean, μ = 40

,

• Standard Deviation, σ = 8

The z-score formula is given below:

`\begin{gathered} \begin{equation*} z-score=(X-\mu)/(\sigma)\text{ where }\begin{cases}{X=Raw\;Score} \\ {\mu=mean} \\ {\sigma=Standard\;Deviation}\end{cases} \end{equation*} \\ \implies X=z\sigma+\mu \end{gathered}`

The values of X are calculated below:

`\begin{gathered} \text{When z=1: }X=1(8)+40=8+40=48 \\ \text{When z=0.25: }X=0.25(8)+40=2+40=42 \\ \begin{equation*} \text{When z=1.50: }X=1.50(8)+40=12+40=52 \end{equation*} \\ \text{When z=-0.50: }X=-0.50(8)+40=-4+40=36 \\ \text{When z=-1.25: }X=-1.25(8)+40=-10+40=30 \\ \text{When z=-2.50}X=-2.50(8)+40=-20+40=20 \end{gathered}`