Question

Evelyn earned a score of 86 on Exam A that had a mean of 71 and a standard deviation of 20. She is about to take Exam B that has a mean of 550 and a standard deviation of 40. How well must Evelyn score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.

Answer 1

580

Explanation:

Assuming that the answer should be in terms of z scores, we can calculate the z score as

z = (observed value - mean)/(standard deviation)

For the first exam, the observed value is 86, the mean is 71, and the standard deviation is 20. The z score fot that exam is

z = (86-71)/20 = 0.75

Then, for the second exam, Evelyn has to do equivalently well, so the z score must be the same. Therefore, we have

0.75 = (observed score - 550)/40

multiply both sides by 40 to remove a denominator

0.75 * 40 = observed score - 550

add 550 to both sides to isolate the observed score

0.75 * 40 + 550 = observed score = 580