Question

1. on a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 40. find the z - score of a person who scored 330 on the exam.

given
$mu = 300$
$sigma=40$
$x = 330$

Explanation:

Step1: Recall z - score formula

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

Step2: Substitute given values

We are given $\mu = 300$, $\sigma = 40$, and $x = 330$. Substitute these values into the formula: $z=\frac{330 - 300}{40}$.

Step3: Calculate the numerator

$330-300 = 30$. So, $z=\frac{30}{40}$.

Step4: Simplify the fraction

$\frac{30}{40}=\frac{3}{4}=0.75$.

Answer:

$0.75$