Question

4. For a population with μ = 40 and σ = 8:a. Find the z-score for each of the following X values.(Note: You should be able to find these values us-ing the definition of a z-score. You should not needto use a formula or do any serious calculations.)X = 44X = 38X = 48X = 34X = 56X = 32

Answer 1

We need to find the z-score for each value of x given.

The z-score z of value x belonging to a population with mean μ and standard deviation σ is defined as:

`z=(x-\mu)/(\sigma)`

In this problem, we have:

`\begin{gathered} \mu=40 \\ \\ \sigma=8 \end{gathered}`

Thus, for each value of x given, we obtain:

`\begin{gathered} z(x=44)=(44-40)/(8)=(4)/(8)=0.5 \\ \\ z(x=38)=(38-40)/(8)=(-2)/(8)=-0.25 \\ \\ z(x=48)=(48-40)/(8)=(8)/(8)=1 \\ \\ z(x=34)=(34-40)/(8)=(-6)/(8)=-0.75 \\ \\ z(x=56)=(56-40)/(8)=(16)/(8)=2 \\ \\ z(x=32)=(32-40)/(8)=(-8)/(8)=-1 \end{gathered}`

Answer

X = 44: 0.5

X = 38: -0.25

X = 48: 1

X = 34: -0.75

X = 56: 2

X = 32: -1