 # a. Identify the conditions would it be reasonable to use z-scores to compare the yapafw 2021-11-21 Answered
a. Identify the conditions would it be reasonable to use z-scores to compare the standings of the student on the two tests relative to the other students in the graduating class.
Given info:
The mean SAT math score is 528 with a standard deviation of 105. The mean SAT verbal score is 475 with standard deviation is 98. A student in the graduating class scored 740 on SAT math and 715 on SAT verbal.
b. To identify the test did the student do better.

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a) Justification:
If the distributions of the two data have same shape then it is reasonable to use z-scores to compare the standings of the stident on the two tests relative to the other students in the graduating class.
It is reasonable to use z-scores to compare the standings of the students on the two tests relative to the other students in the graduating class, if the distributions of the math and verbal SAT scores for the graduating class have approximately same shape.
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b) Calculation:
The formula for finding z-score is,
$$\displaystyle{z}={\frac{{{X}-\mu}}{{\sigma}}}$$
For math SAT:
Substitute $$\displaystyle{X}={740},\mu={528}$$ and $$\displaystyle\sigma={105}$$ in z-score formula
$$\displaystyle{z}={\frac{{{740}-{528}}}{{{105}}}}$$
$$\displaystyle={2.01}$$
For verbal SAT:
$$\displaystyle{z}={\frac{{{X}-\mu}}{{\sigma}}}$$
Substitute $$\displaystyle{X}={715},\mu={528}$$ and $$\displaystyle\sigma={105}$$ in z-score formula
$$\displaystyle{z}={\frac{{{715}-{528}}}{{{105}}}}$$
$$\displaystyle={2.45}$$
Here, the student's z-score on the verbal SAT is greater than the students z-score on the math SAT. Thus, the student did better on the verbal SAT relative to the other students in the class.