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Sagot :
We need to calculate first for the z-score of Angel on Exam A. The z-score can be computed using the equation:
[tex]z=\frac{x-\operatorname{mean}}{\text{standard deviation}}[/tex]Given the mean, score (represented by x), and the standard deviation, Angel's z-score in exam A is computed as follows:
[tex]\begin{gathered} z=\frac{174-150}{40} \\ z=\frac{24}{40}=0.6 \end{gathered}[/tex]We now derive an equation solving for x to compute the needed score of Angel on Exam B so that she has the same performance as Exam A.
[tex]\begin{gathered} x-\operatorname{mean}=z\cdot\text{standard deviation} \\ x=\operatorname{mean}+z\cdot\text{standard deviation} \end{gathered}[/tex]Using the z score computed on Exam A plus the mean and standard deviation for Exam B, the minimum points Angel needed will be:
[tex]\begin{gathered} z=(550)+(0.6\cdot40) \\ z=550+24=574 \end{gathered}[/tex]Therefore, Angel needs a score of 574 on exam B so that he can do equivalently as well as Exam A.
Answer: 574 points
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