Question

Christopher earned a score of 480 on Exam A that had a mean of 500 and a standarddeviation of 20. He is about to take Exam B that has a mean of 500 and a standarddeviation of 50. How well must Christopher score on Exam B in order to doequivalently well as he did on Exam A? Assume that scores on each exam arenormally distributed.

Answer 1

Exam A

mean = 500

standard deviation = 20

`\begin{gathered} Z=(x-\mu)/(\sigma) \\ Z=(480-500)/(20) \\ Z=-(20)/(20)=-1 \end{gathered}`

since scores on each exam are normally distributed

then z score = -1

Exam B

mean = 500

standard deviation = 50

`\begin{gathered} Z=(x-\mu)/(\sigma) \\ -1=(x-500)/(50) \\ -50=x-500 \\ -50+500=x \\ x=450 \end{gathered}`

Therefore Christopher score on Exam B = 450