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.
To calculate the z-score, we use the formula:
z = (X - μ) / σ
where:
X = the value we are trying to find the z-score for (355 pages)
μ = the mean (average page count) = 550 pages
σ = the standard deviation = 112 pages
Plugging these values into the formula, we get:
z = (355 - 550) / 112
z = -195 / 112
z ≈ -1.7411
Interpreting this z-score, we can say that a book with 355 pages is approximately 1.7411 standard deviations below the average page count of books in the library.