Question

1. on a standardized exam, the scores are normally distributed with a mean of 135 and a standard deviation of 25. find the z-score of a person who scored 160 on the exam.

Explanation:

Step1: Recall 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: Identify values

We are given that $x = 160$, $\mu=135$, and $\sigma = 25$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{160 - 135}{25}$.
First, calculate the numerator: $160-135 = 25$.
Then, divide by the standard deviation: $z=\frac{25}{25}=1$.

Answer:

1