Answer:
a) see the attached
b) -0.1213
c) 0.0653
d) 0.0171
e) EOC
Step-by-step explanation:
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 <em>why</em> 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.
