Answer:
a) -0.75
b) -1.5
c) -3
Step-by-step explanation:
Population Mean = u = 40
Standard deviation = s = 8
We are given a value to convert it into z-score with different sample sizes.
For a given sample size "n", the formula to calculate the z-score is:
[tex]z=\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]
For x = 34 and n=1, we get:
[tex]z-score=\frac{34-40}{\frac{8}{\sqrt{1} } } = -0.75[/tex]
For x = 34 and n = 4, we get:
[tex]z-score=\frac{34-40}{\frac{8}{\sqrt{4} } } = -1.5[/tex]
For x = 34 and n = 16, we get:
[tex]z-score=\frac{34-40}{\frac{8}{\sqrt{16} } } = -3[/tex]
Answer:
(a) -0.75
(b) -1.5
(c) -3
Step-by-step explanation:
The formula for calculating z-score is :
[tex]Z= \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} } [/tex]
(a) Â [/tex]\bar{x} [/tex] = 34
μ = 40
n = 1
σ = 8
Putting all values,
Z = \frac{34-40}{\frac{8}{\sqrt{1}} }
⇒ Z= -0.75
(b) Â Z = \frac{34-40}{\frac{8}{\sqrt{4}} }
⇒ Z= -1.5
(c) Â Z = \frac{34-40}{\frac{8}{\sqrt{16}} }
⇒ Z= -3
