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Wyatt earned a score of 45 on Exam A that had a mean of 35 and a standard deviationof 5. He is about to take Exam B that has a mean of 100 and a standard deviation of25. How well must Wyatt score on Exam B in order to do equivalently well as he didon Exam A? Assume that scores on each exam are normally distributed.

Answer :

SOLUTION

Since the scores are normally distributed, we will first obtain the Z score from Exam A, and then use it to find the score required from Exam B to meet that same Z score.

[tex]Z=\frac{X-M}{\sigma}[/tex]

For Exam A, X(score)=45, M(mean)=35, S.D=5

Z will be:

[tex]\begin{gathered} Z=\frac{45-35}{5} \\ Z=\frac{10}{5} \\ Z=+2 \end{gathered}[/tex]

So to obtain, the score (X) for exam B, that will give us the same Z score.

For Exam B, X(score)=unknown, M(mean)=100, S.D= 25

[tex]Z=2=\frac{X-100}{25}[/tex][tex]\text{Cross multiply}[/tex][tex]\begin{gathered} 50=x-100 \\ 50+100=x \\ 150=x \end{gathered}[/tex]

So Wyatt must score 150 in exam B in order to do equivalently well as he

did on exam A.

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