ANSWER
The z-score is 2.
EXPLANATION
The z-score for a data set that is normally distributed is calculated using the formula:
[tex]z = \frac{x - \bar x}{ \sigma} [/tex]
where
[tex]\bar x[/tex]
is the mean and
[tex] \sigma[/tex]
is the standard deviation of the distribution.
From the given information the test score is 85.
This implies that,
[tex]x = 85[/tex]
The mean is 75.
[tex]\bar x = 75[/tex]
The standard deviation is 5.
We substitute the values into the formula to get,
[tex]z = \frac{85 - 75}{5} [/tex]
This implies that
[tex]z = \frac{10}{5} [/tex]
Therefore the z-score is
[tex]z = 2[/tex]
