Question

In a population with a standard deviation of σ = 5, a score of X = 44 corresponds to a z-score of z = 2.00. What is the population mean?

Answer 1

Given:

The standard deviation, σ = 5.

The observed value, X=44.

The z score, z=2.00.

The expression for z-score can be written as,

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

Here, μ is the mean.

Substitute the known values in the above equation to find mean μ.

`\begin{gathered} 2=(44-\mu)/(5) \\ 5*2=44-\mu \\ 10=44-\mu \\ \mu=44-10 \\ \mu=34 \end{gathered}`

Therefore, the population mean is 34.