Answer:
• z=-1.00, X=70
,
• z=0.75, X=105
,
• z=0.50, X=100
,
• z=-1.25, X=65
,
• z=-1.50, C=60
,
• z=2.60, X=142
Explanation:
Given a sample whose:
• Mean = 90
,
• Standard Deviation = 20
To find the X-values from the given z-scores, we use the formula below:
[tex]X=z\sigma+\mu\text{ where }\begin{cases}{z=z-score} \\ {\mu=mean} \\ {\sigma=Standard\;Deviation}\end{cases}[/tex]
(a)z=-1.00
[tex]X=-1.00(20)+90=70[/tex]
The X-value is 70.
(b)z=0.75
[tex]X=0.75(20)+90=15+90=105[/tex]
The X-value is 105.
(c)z=0.50
[tex]X=0.50(20)+90=10+90=100[/tex]
The X-value is 100.
(d)z=-1.25
[tex]X=-1.25(20)+90=-25+90=65[/tex]
The X-value is 65.
(e)z=-1.50
[tex]X=-1.50(20)+90=-30+90=60[/tex]
The X-value is 60.
(e)z=2.60
[tex]X=2.60(20)+90=52+90=142[/tex]
The X-value is 142.
