Question

the grades on a history midterm at almond are roughly symmetric with μ = 85 and σ = 2.0. michael scored 86 on the exam. find the z-score for michaels 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 $x = 86$, $\mu=85$, and $\sigma = 2.0$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{86 - 85}{2.0}$.

Step4: Calculate the result

First, calculate the numerator: $86 - 85=1$. Then divide by the denominator: $z=\frac{1}{2.0}=0.50$.

Answer:

0.50