4. Which student scored better than other test takers? Why?

Although Jonce had the higher raw score, their z-score is 2/3 (~75 percentile), whereas Taskika's z-score is 2 (~97.5 percentile). Tashika's raw score is lower, but they did better than 97.5% of their classmates.

Standard scores (aka. z-scores)

A standard score (or z-score) measures how many standard deviations a score is from the mean. It is computed by…

\( z = \dfrac{x - \mu}{\sigma} \)

… where \(x\) is a data point, \(\mu\) is the mean, \(\sigma\) is the standard deviation. In the normal distribution above, \(\mu\) has \(z=0\), \(\mu + \sigma\) has \(z = 1\), and so on.

Curving a test

An exam was normally distributed with μ = 75 and σ = 17.6. The professor wants to base grades on standard deviations. Please complete the following: