Question

A sample has a mean of M = 90 and a standard devia-tion of s 20.=a. Find the z-score for each of the following X values.X = 95X = 80X = 98X = 88X = 105X = 76

Answer 1

`\begin{gathered} X=95,z=0.25 \\ X=80,z=-0.5 \\ X=98,z=0.4 \\ X=88,z=-0.1 \\ X=105,z=0.75 \\ X=76,z=-0.7 \end{gathered}`

Explanation:

Given a sample with the following:

• Mean,M = 90

,

• Standard deviation, s = 20

To find the z-score for each of the given X values, we use the formula below:

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

The z-scores are calculated below:

`\begin{gathered} \text{When X=95, }z=(95-90)/(20)=(5)/(20)=0.25 \\ \text{When X=80, }z=(80-90)/(20)=(-10)/(20)=-0.5 \\ \text{When X=98, }z=(98-90)/(20)=(8)/(20)=0.4 \end{gathered}`
`\begin{gathered} \text{When X=88,}z=(88-90)/(20)=(-2)/(20)=-0.1 \\ \text{When X=105, }z=(105-90)/(20)=(15)/(20)=0.75 \\ \text{When X=76, }z=(76-90)/(20)=(-14)/(20)=-0.7 \end{gathered}`