Question

1. the length of a book with a fictional story is normally distributed with a mean of 350 pages and a stand deviation of 50 pages. find the data item in this distribution that corresponds to a z - score of - 1.5.

Explanation:

Step1: Recall the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data item, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
We are given that \(\mu = 350\), \(\sigma=50\), and \(z=- 1.5\).

Step2: Solve the z - score formula for \(x\)

Starting with \(z=\frac{x-\mu}{\sigma}\), we can multiply both sides by \(\sigma\): \(z\sigma=x - \mu\).
Then add \(\mu\) to both sides to get \(x=\mu+z\sigma\).
Substitute the given values: \(x = 350+(-1.5)\times50\).
First, calculate \((-1.5)\times50=-75\).
Then \(x=350 - 75\).

Answer:

\(275\)