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For a population with a mean of u = 40 and a standarddeviation of o = 8, find the z-score corresponding toeach of the following samples.a. X = 34 for a sample of n = 1 scoreb. x = 34 for a sample of n = 4 scoresc. x = 34 for a sample of n = 16 scores

Respuesta :

Solution:

Given the mean and standard deviation;

[tex]\mu=40,\sigma=8[/tex]

The z-score formula is;

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

(a)

[tex]\begin{gathered} x=34,n=1 \\ \\ z=\frac{34-40}{\frac{8}{\sqrt{1}}} \\ \\ z=-0.75 \end{gathered}[/tex]

(b)

[tex]\begin{gathered} x=34,n=4 \\ \\ z=\frac{34-40}{\frac{8}{\sqrt{4}}} \\ \\ z=-1.5 \end{gathered}[/tex]

(c)

[tex]\begin{gathered} x=34,n=16 \\ \\ z=\frac{34-40}{\frac{8}{\sqrt{16}}} \\ \\ z=-3 \end{gathered}[/tex]

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