Question

The books at a certain library are found to have an average page count of 550 pages, with a standard deviation of 112 pages. Select the option that correctly calculates and interprets the z-score for a book that is 355 pages long.(1 point)
Responses

The book's page count is 195 standard deviations below the mean.
The book's page count is 195 standard deviations below the mean.

The book's page count is 1.741 standard deviations above the mean.
The book's page count is 1.741 standard deviations above the mean.

The book's page count is 195 standard deviations above the mean.
The book's page count is 195 standard deviations above the mean.

The book's page count is 1.741 standard deviations below the mean.

Answer 1

To calculate the z-score for the book with a page count of 355 pages, we use the formula for the z-score:

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

where:
- \(X\) is the value (the page count of the book),
- \(\mu\) is the mean,
- \(\sigma\) is the standard deviation.

Given:
- \(X = 355\)
- \(\mu = 550\)
- \(\sigma = 112\)

Plugging in the values:

\[
z = \frac{(355 - 550)}{112} = \frac{-195}{112} \approx -1.741
\]

Thus, the z-score is approximately \(-1.741\).

This means that the book's page count is **1.741 standard deviations below the mean**.

The correct response is:

**The book's page count is 1.741 standard deviations below the mean.**