Question

Jaxson earned a score of 870 on Exam A that had a mean of 750 and a standarddeviation of 100. He is about to take Exam B that has a mean of 700 and a standarddeviation of 100. How well must Jaxson score on Exam B in order to do equivalentlywell as he did on Exam A? Assume that scores on each exam are normally distributed.

Answer 1

To do equivalently well in exam B, Jaxson has to earn a score of 820

Here, we simply need to calculate the score on exam B that has same z-score as exam A

Mathematically, we can calculate the z-score as follows;

$\begin{gathered} z-\text{score = }\frac{x-\mu}{\sigma} \\ \mu\text{ = mean} \\ x\text{ = score} \\ \sigma\text{ = standard deviation} \\ \text{for Exam A;} \\ z-\text{score = }\frac{870-750}{100}\text{ =}1.2 \\ we\text{ want x for exam B;} \\ 1.2\text{ = }\frac{x-700}{100} \\ 100(1.2)\text{ = x-700} \\ 120\text{ = x-700} \\ x\text{ = 120 + 700} \\ x\text{ = 820} \end{gathered}$