John recently did a class test in each of three subjects - HSC - SSCE Mathematics Advanced - Question 4 - 2020 - Paper 1

For Commerce, we use the same formula:

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

Where:

• $X$ is John's score (80)
• $\mu$ is the mean (65)
• $\sigma$ is the standard deviation (5)

Calculating:

$Z = \frac{80 - 65}{5} = \frac{15}{5} = 3$

The Z-score for Commerce is $3$.

For Music, we apply the Z-score formula:

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

Where:

• $X$ is John's score (74)
• $\mu$ is the mean (50)
• $\sigma$ is the standard deviation (12)

Calculating gives:

$Z = \frac{74 - 50}{12} = \frac{24}{12} = 2$

The Z-score for Music is $2$.