Question

suppose the scores on an exam are normally distributed with a mean $mu = 75$ points and standard deviation $sigma = 8$ points. what is the exam score for an exam whose z - score is 1.25? a. 65 b. 75 c. 85 d. 0.8944 e. 0.1056

Explanation:

Step1: Recall the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $z$ is the z - score, $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to find $x$, so we can re - arrange the formula to $x = z\sigma+\mu$.

Step2: Substitute the given values

We are given that $\mu = 75$, $\sigma = 8$, and $z = 1.25$. Substitute these values into the formula $x=z\sigma+\mu$.
$x=1.25\times8 + 75$.
First, calculate $1.25\times8$: $1.25\times8=10$.
Then, calculate $10 + 75$: $x=85$.

Answer:

C. 85