Question

Elijah earned a score of 228 on Exam A that had a mean of 200 and a standarddeviation of 40. He is about to take Exam B that has a mean of 550 and a standarddeviation of 100. How well must Elijah 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

Lets start finding the z-score for the first score (Exam A):

$z=\frac{228-200}{40}$$z=\frac{28}{40}=\frac{14}{20}=\frac{7}{10}$

Now lets find the score of exam B in order to do equivalently well as on Exam A (same z-score):

$z=\frac{x-550}{100}$$\frac{7}{10}=\frac{x-550}{100}$$\frac{7}{10}\cdot100=x-550$$70+550=x$$620=x$

Elijah must score 620 on exam B in order to do equivalently well as on Exam A