on a unit test in a statistics class, the teacher determines that the mean test grade was 77.5 with a…

Answer:

D. 90

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. We want to solve for $x$. Rearranging the formula gives $x = z\sigma+\mu$.

Step2: Substitute given values

We are given that $\mu = 77.5$, $\sigma=5.2$, and $z = 2.4$. Substitute these values into the formula: $x=2.4\times5.2 + 77.5$.

Step3: Calculate the product

First, calculate $2.4\times5.2=12.48$.

Step4: Calculate the value of $x$

Then, $x=12.48 + 77.5=89.98$.

Step5: Round to the nearest whole number

Rounding $89.98$ to the nearest whole number gives $90$.