Question

the grades on a language midterm at santa rita are roughly symmetric with $\mu = 77$ and $\sigma = 3.5$.
tiffany scored 80 on the exam.
find the z-score for tiffanys 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 individual score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We know that $x = 80$, $\mu=77$, and $\sigma = 3.5$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{80 - 77}{3.5}=\frac{3}{3.5}\approx0.86$ (rounded to two decimal places).

Answer:

$0.86$