Answer :
Notation:
μ = mean
σ = standard deviation
Exam A:
[tex]\begin{gathered} \mu=100 \\ \sigma=20 \end{gathered}[/tex]The score of the exam is 64, so we calculate the z-score given that scores on the exam are normally distributed. The formula of the z-score is:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]Now, for X = 64:
[tex]Z=\frac{64-100}{20}=-1.8[/tex]Exam B:
[tex]\begin{gathered} \mu=600 \\ \sigma=40 \end{gathered}[/tex]Now, we need to find a z-score equal to that of the score on Exam A. This z-score is -1.8, and the score on exam B should be:
[tex]\begin{gathered} -1.8=\frac{X-600}{40} \\ -72=X-600 \\ \therefore X=528 \end{gathered}[/tex]The score on exam B should be 528 in order to do equivalently well as he did on Exam A