Question

d) a set of exam scores has a z - score of -0.4 with a standard deviation of 2. if your score was 81%, what is the mean?

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $z$ is the z - score, $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Rearrange the formula to solve for the mean

We can rewrite the formula as $\mu=x - z\sigma$.

Step3: Substitute the given values

We are given that $z=- 0.4$, $\sigma = 2$, and $x = 81$. Substituting these values into the formula $\mu=x - z\sigma$, we get $\mu=81-(-0.4)\times2$.

Step4: Calculate the mean

First, calculate $(-0.4)\times2=-0.8$. Then, $\mu=81 + 0.8=81.8$.

Answer:

81.8