Question

the grades on a geometry midterm at springer are roughly symmetric with μ = 68 and σ = 2.0. emily scored 69 on the exam. find the z-score for emilys 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 $x = 69$, $\mu=68$, and $\sigma = 2.0$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{69 - 68}{2.0}$.

Step4: Calculate the result

First, calculate the numerator: $69 - 68=1$. Then divide by the standard deviation: $z=\frac{1}{2.0}=0.50$.

Answer:

0.50