Question

5) A data set has a mean of 68.42 and a standard deviation of 7.91. An element in this set is 57. What is the z-score of 57? Round the answer to the nearest hundredth.

Answer 1

To find the z-score we use the following formula:

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

Where x is the data point or the element, in this case:

`x=57`

μ is the mean:

`\mu=68.42`

and σ is the standard deviation:

`\sigma=7.91`

--> Substituting these three values into the z-score formula

`z-\text{score}=(57-68.42)/(7.91)`

Solving the operations:

`\begin{gathered} z-\text{score}=(-11.72)/(7.91) \\ \\ z-\text{score}=-1.48167 \end{gathered}`

Finally, we need to round to the nearest hundredth (2 decimal places):

`z-\text{score}=-1.48`

Answer: -1.48