On a test, Zac’s mark corresponded to a z-score of 2 - HSC - SSCE Mathematics Standard - Question 8 - 2021 - Paper 1

To find Zac's actual mark (X), we can use the z-score formula:

$z = \frac{X - \mu}{\sigma}$

where:

• $z$ is the z-score (2 in this case)
• $\mu$ is the mean (63)
• $\sigma$ is the standard deviation (8)

Rearranging the formula gives: $X = z \cdot \sigma + \mu$

Substituting the values: $X = 2 \cdot 8 + 63$ $X = 16 + 63$ $X = 79$