Question

on a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 25. find the z - score of a person who scored 260 on the exam.

Explanation:

Step1: Recall the z - score formula

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

Given that \(x = 260\), \(\mu=300\), and \(\sigma = 25\). Then \(z=\frac{260 - 300}{25}\).

Step3: Calculate the numerator

\(260-300=-40\). So \(z=\frac{-40}{25}\).

Step4: Simplify the fraction

\(\frac{-40}{25}=-\frac{8}{5}=-1.6\)

Answer:

\(-1.6\)