To determine which expression Din should use to find the [tex]$z$[/tex]-score of her test score, we first need to recall the formula for calculating a [tex]$z$[/tex]-score. The [tex]$z$[/tex]-score is a way of describing how far a particular score is from the mean in terms of standard deviations.
The formula for the [tex]$z$[/tex]-score is given by:
[tex]$
z = \frac{x - \mu}{\sigma}
$[/tex]
where:
- [tex]\( x \)[/tex] is the value of the score,
- [tex]\( \mu \)[/tex] is the mean,
- [tex]\( \sigma \)[/tex] is the standard deviation.
Given:
- [tex]\( \mu = 83 \)[/tex],
- [tex]\( \sigma = 5 \)[/tex],
- [tex]\( x = 92 \)[/tex].
Now, substitute these values into the formula:
[tex]$
z = \frac{92 - 83}{5}
$[/tex]
Thus, the correct expression Din should use to find the [tex]$z$[/tex]-score of her test score is:
[tex]$
z = \frac{92 - 83}{5}
$[/tex]
Choosing the correct option:
[tex]$
z = \frac{92 - 83}{5}
$[/tex]
