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

Given the mean and standard deviation;

`\mu=40,\sigma=8`

The z-score formula is;

`z=(x-\mu)/((\sigma)/(√(n)))`

(a)

`\begin{gathered} x=34,n=1 \\ \\ z=(34-40)/((8)/(√(1))) \\ \\ z=-0.75 \end{gathered}`

(b)

`\begin{gathered} x=34,n=4 \\ \\ z=(34-40)/((8)/(√(4))) \\ \\ z=-1.5 \end{gathered}`

(c)

`\begin{gathered} x=34,n=16 \\ \\ z=(34-40)/((8)/(√(16))) \\ \\ z=-3 \end{gathered}`