Question

the grades on a math midterm at gardner bullis are roughly symmetric with μ = 76 and σ = 4.5.
daniel scored 64 on the exam.
find the z-score for daniels 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 $x = 64$, $\mu=76$, and $\sigma = 4.5$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{64 - 76}{4.5}$.
First, calculate the numerator: $64-76=- 12$.
Then, divide by the standard deviation: $z=\frac{-12}{4.5}\approx - 2.67$ (rounded to two decimal places).

Answer:

-2.67