P5a College entrance examination is a standard test. The data from this test is
ID: 3153683 • Letter: P
Question
P5a
College entrance examination is a standard test. The data from this test is used by colleges to determine the chance of success of their incoming students. This test is standard, so the mean of the scores on this test is 500 and the standard deviation is 100. Consider George, a student who has earned a score of 650 in this test. Hence the score 650, is his raw score. Using raw score the colleges cannot decide where he stands academically in comparison to his peer. So they need the z-score and they also want to know his standing in comparison to other students taking the same test. So first find the z-score for George and then find what percentage of students in his cohort performed better than him? (Hint you need to find area above. Do not forget to multiply by 100 to get percentage. If you do not multiply by 100 you will have probability or proportion)
Explanation / Answer
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 650
u = mean = 500
s = standard deviation = 100
Thus,
z = (x - u) / s = 1.5 [ANSWER, Z SCORE]
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Thus, using a table/technology, the right tailed area of this is
P(z > 1.5 ) = 0.066807201 = 6.68% [ANSWER]
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