Question

In a certain book series, the average number of pages in each book is 315 pages with a standard deviation of 23.

Ayna recently finished a book in the series that was 330 pages long. Calculate the z-score of this book to the nearest hundredth.

(1 point)
z =
𝑧

=

Answer 1

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 \(z = 0.65\).