Question

the grades on a math midterm at loyola are roughly symmetric with μ = 68 and σ = 5.5.
jessica scored 66 on the exam.
find the z-score for jessicas exam grade. round to two decimal places.

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 dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We know that $x = 66$, $\mu=68$, and $\sigma = 5.5$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{66 - 68}{5.5}=\frac{- 2}{5.5}$.

Step4: Calculate and round

Calculate $\frac{-2}{5.5}\approx - 0.36$ (rounded to two decimal places).

Answer:

-0.36