To calculate the z-score for the book that Ayna recently finished, you can use the following formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \(X\) is the value (the number of pages in Ayna's book).
- \(\mu\) is the mean (average number of pages in the series).
- \(\sigma\) is the standard deviation.
Given:
- \(X = 330\) pages (the book Ayna finished)
- \(\mu = 315\) pages (average number of pages)
- \(\sigma = 23\) pages (standard deviation)
Now, plug in the values:
\[ z = \frac{(330 - 315)}{23} = \frac{15}{23} \approx 0.652173913 \]
Now, rounding to the nearest hundredth:
\[ z \approx 0.65 \]
Thus, the z-score of the book is approximately \(z = 0.65\).