We first look at the z-score on Exam A. The z-score can be computed as follows:
[tex]\begin{gathered} z=\frac{x-\operatorname{mean}}{\text{standard dev}} \\ z=\frac{152-200}{20}=-2.4 \end{gathered}[/tex]Using the formula for z-score, we derive the equation solving for x to find the score of Sebastian in Exam B, as follows:
[tex]\begin{gathered} x-mean=z\cdot\text{standard deviation} \\ x=\operatorname{mean}+z\cdot\text{standard deviation} \end{gathered}[/tex]The z-score is already computed above. Also, the mean and standard deviation on Exam B is already given. We can plug it on the derived equation and solve for x, as follows:
[tex]\begin{gathered} x=300+(25\cdot-2.4) \\ x=300+(-60)=240 \end{gathered}[/tex]Therefore, Sebastian must get a minimum score of 240 so that he can do equivalently as well as he did on Exam A.
Answer: 240 pts on Exam B
