Question

Books in the library are found to have an average length of 350 pages with a standard deviation of 100 pages. What is the z-score corresponding to a book with 280 pages?

A) -0.7
B) -2.0
C) 1.0
D) 0.2

Answer 1

The z-score corresponding to a book with 280 pages is calculated using the formula (X - μ) / σ, and with the given mean and standard deviation, the z-score is found to be -0.7.

Step-by-step explanation:

To calculate the z-score for the book-length of 280 pages, we use the formula:

Z = (X - μ) / σ

Where:

• X is the value for which we are calculating the z-score (280 pages in this case).
• μ (mu) is the mean of the data set (350 pages).
• σ (sigma) is the standard deviation of the data set (100 pages).

Plugging in the values, we get:

Z = (280 - 350) / 100

Z = -70 / 100

Z = -0.7

Therefore, the z-score corresponding to a book with 280 pages is -0.7, which corresponds to option A). This z-score indicates how many standard deviations 280 pages deviate from the mean, delineating the book's position concerning the average book length within the dataset.