A test has a mean of 75 and a standard deviation of 8. What is the z-score for 91?

Problem: Find the z-score for a value of $x = 91$ in a distribution with a mean $\mu = 75$ and a standard deviation $\sigma = 8$.

Steps

1. State the z-score formula
   $$z = \frac{x - \mu}{\sigma}$$
2. Substitute the given values
   $$z = \frac{91 - 75}{8}$$
3. Subtract the numerator
   $$z = \frac{16}{8}$$
4. Divide
   $$z = 2$$