Question

on a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 20. find the z - score of a person who scored 285 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 \(x = 285\), \(\mu=300\), and \(\sigma = 20\). Then \(z=\frac{285 - 300}{20}\).

Step3: Calculate the numerator

\(285-300=-15\). So \(z=\frac{-15}{20}\).

Step4: Simplify the fraction

\(\frac{-15}{20}=-\frac{3}{4}=- 0.75\).

Answer:

\(-0.75\)