Question

Allison earned a score of 775 on Exam A that had a mean of 700 and a standarddeviation of 50. She is about to take Exam B that has a mean of 350 and a standarddeviation of 100. How well must Allison score on Exam B in order to do equivalentlywell as she did on Exam A? Assume that scores on each exam are normallydistributed

Answer 1

The formula for the z-score is,

$z=\frac{x-\mu}{\sigma}$

Determine the z-score for Exam A.

$\begin{gathered} z_A=\frac{775-700}{50} \\ =-\frac{75}{50} \\ =-1.5 \end{gathered}$

For equivalent the z score of both the exams must be equal.

Determine the value of x for z = -1.5.

$\begin{gathered} -1.5=\frac{x-350}{100} \\ x-350=150 \\ x=350+150 \\ =500 \end{gathered}$

So Allison must score 500 marks in Exam B in order to do equivalently

well as she did on Exam A.