Answer
• a. Z = 0.20
,• b. Z = –0.60
,• c. Z = 3.00
Explanation
Given
• μ = 80
,• σ = 20
The Z-score formula is given by:
[tex]Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]a.
Considering a mean of x = 82 and a sample of n = 4, then:
[tex]Z=\frac{82-80}{\frac{20}{\sqrt{4}}}=0.20[/tex]b.
Considering that x = 76 and n= 9:
[tex]Z=\frac{76-80}{\frac{20}{\sqrt{9}}}=-0.60[/tex]c.
Considering that x = 90 and n= 36:
[tex]Z=\frac{90-80}{\frac{20}{\sqrt{36}}}=3[/tex]
