Question

Given 𝜇 = 45, and 𝜎 = 5.5. (7 points)

a. What is the raw score when 𝑧 = −1.57?

b. What is the raw score when 𝑧 = 2.09?

c. What is the raw score when −0.48 < 𝑧 < 1.4?

d. What is the raw score when −2.17 < 𝑧 < 1.79? e. What is the raw score when 𝑧 = 0.09?

Answer 1

a.

$$z =\dfrac{x-\mu}{\sigma}= −1.57$$

$$x=45-1.57(5.5)=36.365$$

b.

$$z =\dfrac{x-\mu}{\sigma}= 2.09$$

$$x=45+2.09(5.5)=56.495$$

c.

$$z =\dfrac{x-\mu}{\sigma}= −0.48$$

$$x=45-0.48(5.5)=42.36$$

$$z =\dfrac{x-\mu}{\sigma}= 1.4$$

$$x=45+1.4(5.5)=52.7$$

$$42.36<x<52.7$$

d.

$$z =\dfrac{x-\mu}{\sigma}= −2.17$$

$$x=45-2.17(5.5)=33.065$$

$$z =\dfrac{x-\mu}{\sigma}= 1.79$$

$$x=45+1.79(5.5)=54.845$$

$$33.065<x<54.845$$

e.

$$z =\dfrac{x-\mu}{\sigma}= 0.09$$

$$x=45+0.09(5.5)=45.495$$