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

Answer:

• (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:

$\begin{equation*} z-score=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}{X=Raw\;Score} \\ {\mu=mean} \\ {\sigma=Standard\;Deviation}\end{cases} \end{equation*}$

(a) μ = 50 and σ = 20

$z=\frac{30-50}{20}=-\frac{20}{20}=-1$

The z-score is -1.

(b) μ = 50 and σ = 10

$z=\frac{30-50}{10}=-\frac{20}{10}=-2$

The z-score is -2.

(c)μ = 20 and σ = 5

$z=\frac{30-20}{5}=\frac{10}{5}=2$

The z-score is 2.

(d)μ = 20 and σ = 2

$z=\frac{30-20}{2}=\frac{10}{2}=5$

The z-score is 5.