Question

the grades on a chemistry midterm at loyola are roughly symmetric with μ = 67 and σ = 5.5. tiffany scored 53 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 $x = 53$, $\mu=67$, and $\sigma = 5.5$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{53 - 67}{5.5}$.
First, calculate the numerator: $53-67=- 14$.
Then, divide by the standard deviation: $z=\frac{-14}{5.5}\approx - 2.55$ (rounded to two decimal places).

Answer:

-2.55