Question

Elijah earned a score of 64 on Exam A that had a mean of 100 and a standarddeviation of 20. He is about to take Exam B that has a mean of 600 and a standarddeviation of 40. 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

Notation:

μ = mean

σ = standard deviation

Exam A:

`\begin{gathered} \mu=100 \\ \sigma=20 \end{gathered}`

The score of the exam is 64, so we calculate the z-score given that scores on the exam are normally distributed. The formula of the z-score is:

`Z=(X-\mu)/(\sigma)`

Now, for X = 64:

`Z=(64-100)/(20)=-1.8`

Exam B:

`\begin{gathered} \mu=600 \\ \sigma=40 \end{gathered}`

Now, we need to find a z-score equal to that of the score on Exam A. This z-score is -1.8, and the score on exam B should be:

`\begin{gathered} -1.8=(X-600)/(40) \\ -72=X-600 \\ \therefore X=528 \end{gathered}`

The score on exam B should be 528 in order to do equivalently well as he did on Exam A