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=(228-200)/(40)`
`z=(28)/(40)=(14)/(20)=(7)/(10)`

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

`z=(x-550)/(100)`
`(7)/(10)=(x-550)/(100)`
`(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