Question

the grades on a history midterm at almond are roughly symmetric with μ = 81 and σ = 2.5. luis scored 84 on the exam. find the z-score for luiss 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 $x = 84$, $\mu=81$, and $\sigma = 2.5$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{84 - 81}{2.5}$.
First, calculate the numerator: $84-81 = 3$.
Then, divide by the standard deviation: $z=\frac{3}{2.5}=1.2$.

Answer:

1.20