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)

Answer 1

To calculate the z-score, you can use the formula:

\[ z = \frac{(X - \mu)}{\sigma} \]

where:

• \( X \) is the value for which you want to calculate the z-score (330 pages),
• \( \mu \) is the mean (average number of pages, which is 315),
• \( \sigma \) is the standard deviation (23 pages).

Plugging in the values:

\[ z = \frac{(330 - 315)}{23} \]

\[ z = \frac{15}{23} \]

Now, calculate the division:

\[ z \approx 0.6521739130 \]

Rounding to the nearest hundredth:

\[ z \approx 0.65 \]

So, the z-score of the book with 330 pages is approximately 0.65.