Question

on a standardized exam, the scores are normally distributed with a mean of 750 and a standard deviation of 100. find the z - score of a person who scored 580 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 raw score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

Given that \(x = 580\), \(\mu=750\), and \(\sigma = 100\).

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Answer:

\(-1.7\)