Question

Hi, can you help me answer this question, please, thank you!

Answer 1

We are asked to determine the Z-score of a data set with a mean of 69.0 inches and a standard deviation of 2.8 inches, to do that we will use the following formula:

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

Where:

`\begin{gathered} \mu=\text{ mean} \\ \sigma=\text{ standard deviation} \\ x=\text{ }observed\text{ value} \end{gathered}`

In this case, the observed value is the height if the man, 74.1 inches tall. Replacing the values we get:

`Z=(74.1-69.0)/(2.8)`

Now we solve the operations:

`Z=(5.1)/(2.8)`

Solving the fraction:

`Z=1.82`

Therefore, the Z-score is 1.82.