Question

on a standardized exam, the scores are normally distributed with a mean of 180 and a standard deviation of 25. find the z - score of a person who scored 130 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 \(x = 130\), \(\mu=180\), and \(\sigma = 25\). Then \(z=\frac{130 - 180}{25}\).

Step3: Calculate the numerator

\(130-180=-50\). So \(z=\frac{- 50}{25}\).

Step4: Calculate the z - score

\(\frac{-50}{25}=-2\).

Answer:

\(-2\)