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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.

Sagot :

Solution

Exam A

mean = 500

standard deviation = 20

[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{480-500}{20} \\ Z=-\frac{20}{20}=-1 \end{gathered}[/tex]

since scores on each exam are normally distributed

then z score = -1

Exam B

mean = 500

standard deviation = 50

[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ -1=\frac{x-500}{50} \\ -50=x-500 \\ -50+500=x \\ x=450 \end{gathered}[/tex]

Therefore Christopher score on Exam B = 450

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