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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

Respuesta :

The formula for the z-score is,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Determine the z-score for Exam A.

[tex]\begin{gathered} z_A=\frac{775-700}{50} \\ =-\frac{75}{50} \\ =-1.5 \end{gathered}[/tex]

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

Determine the value of x for z = -1.5.

[tex]\begin{gathered} -1.5=\frac{x-350}{100} \\ x-350=150 \\ x=350+150 \\ =500 \end{gathered}[/tex]

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

well as she did on Exam A.

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