Question

Nevaeh earned a score of 508 on Exam A that had a mean of 500 and a standarddeviation of 40. She is about to take Exam B that has a mean of 350 and a standarddeviation of 20. How well must Nevaeh score on Exam B in order to do equivalentlywell as she did on Exam A? Assume that scores on each exam are normallydistributed

Answer 1

First we must obtain the relationship between the grade, the mean and the standard deviation of exam A

$\begin{gathered} z=\frac{x-\operatorname{mean}}{\sigma} \\ z_A=\frac{508-500}{40} \\ z_A=0.2 \\ \end{gathered}$

Now we have to find the required score for exam B to reach the same ratio factor z

$\begin{gathered} z_B=z_A \\ 0.2=\frac{x_B-350_{}}{20} \\ x_B=0.2(20)+350 \\ x_B=354 \end{gathered}$

As seen in the calculations, Nevaeh must score 354 on Exam B to equal the score on Exam A