WILL GIVE BRAINLIEST!
1. (14 points) In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation
scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 704.39
and a standard deviation of 36.18. A score of 700 is needed to earn 3 points.
the values of each standard deviation above and below the mean, and make sure to add in the value
of the mean. Answers only are fine.
free
(Graph below)
b. What would be the z-score for a 700 on the EOC? Show work.
C. You can also earn math credit by scoring a remediation free score on the ACT. ACT tests have a mean
value of 21.65 and a standard deviation of 5.36. What would be a Z-score for a 22 on the ACT? Show work.
d. You can also earn math credit by scoring a remediation free score on the SAT. SAT tests have a mean value
of 528 and a standard deviation of 117. What would be a z-score for a 530 on the SAT? Show work.
e. Of the three testing options, which would be statistically easier to earn? Circle the answer and explain
your reasoning. EOC ACT SAT

a) The graph shows the mean and the values at ±1, ±2, and ±3 standard deviations from the mean. Each mark differs from the one below by the value of the standard deviation, 36.18. The central mark is the mean, 704.39.

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b) As you know, the z-score is computed from ...

z = (x -µ)/σ

z = (700 -704.39)/36.18

z = -0.1213

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c) Same formula, different numbers.

z = (22 -21.65)/5.36

z = 0.0653

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d) Likewise, ...

z = (530 -528)/117

z = 0.0171

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e) EOC would be the easiest. The required score has the lowest z-value, so the applicant only needs to do better than a smaller number of peers.

Actually, the answer to this depends on why the thresholds vary. If we assume that the threshold on each test is set appropriate to the desired knowledge and ability, the test-taker would find his knowledge and ability allows him to do better on the ACT than on the other tests.

On the other hand, if the scores are representative of test taker populations all with the same knowledge and ability, less of that knowledge is required to achieve the necessary score on the EOC.