To calculate the z-score for Ayna's book, we can use the z-score formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \(X\) is the value of the observation (the length of the book),
- \(\mu\) is the mean (average) of the distribution,
- \(\sigma\) is the standard deviation.
From the problem, we have:
- \(X = 330\) pages
- \(\mu = 315\) pages (average number of pages)
- \(\sigma = 23\) pages (standard deviation)
Now, substituting these values into the formula:
\[ z = \frac{(330 - 315)}{23} = \frac{15}{23} \approx 0.652173913 \]
Rounding to the nearest hundredth:
\[ z \approx 0.65 \]
Thus, the z-score of the book Ayna finished is approximately 0.65.