Question

1. on a standardized exam, the scores are normally distributed with a mean of 400 and a standard deviation of 50. find the z - score of a person who scored 525 on the exam. m = 400 𝜎 = 50 x = 525 525−400 / 50 125 / 50 = 2.5

Explanation:

Step1: Recall z - score formula

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

Step2: Substitute given values

We are given that $\mu = 400$, $\sigma=50$, and $x = 525$. Substituting these values into the formula, we get $z=\frac{525 - 400}{50}$.

Step3: Calculate the numerator

$525-400 = 125$, so $z=\frac{125}{50}$.

Step4: Simplify the fraction

$\frac{125}{50}=2.5$.

Answer:

$2.5$