Question

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

Answer 1

Solution:

Given the mean and standard deviation;

$\mu=40,\sigma=8$

The z-score formula is;

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

(a)

$\begin{gathered} x=34,n=1 \\ \\ z=\frac{34-40}{\frac{8}{\sqrt{1}}} \\ \\ z=-0.75 \end{gathered}$

(b)

$\begin{gathered} x=34,n=4 \\ \\ z=\frac{34-40}{\frac{8}{\sqrt{4}}} \\ \\ z=-1.5 \end{gathered}$

(c)

$\begin{gathered} x=34,n=16 \\ \\ z=\frac{34-40}{\frac{8}{\sqrt{16}}} \\ \\ z=-3 \end{gathered}$