Question

Find the z-score corresponding to a score of X = 30for each of the following distributions.a. μ = 50 and σ = 20b. μ = 50 and σ = 10c. μ = 20 and σ = 5d. μ = 20 and σ = 2

Answer 1

• (a)-1

,

• (b)-2

,

• (c)2

,

• (d)5

Explanation:

Given X=30, to find the z-scores for each of the distributions, we use the z-score 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*}`

(a) μ = 50 and σ = 20

`z=(30-50)/(20)=-(20)/(20)=-1`

The z-score is -1.

(b) μ = 50 and σ = 10

`z=(30-50)/(10)=-(20)/(10)=-2`

The z-score is -2.

(c)μ = 20 and σ = 5

`z=(30-20)/(5)=(10)/(5)=2`

The z-score is 2.

(d)μ = 20 and σ = 2

`z=(30-20)/(2)=(10)/(2)=5`

The z-score is 5.