P5c College entrance examination is a standard test. The data from this test is

Question

P5c 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 Sherry is a student who has earned a score of 375 in this test. Hence the score 375, is her raw score. Using the raw score the colleges cannot decide where she stands academically in comparison to her peers. So they need the z-score and they also want to know her standing in comparison to other students taking the same test. So first find the z-score for Sherry and then find what percentage of students in her cohort who performed better than him?

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    375      
u = mean =    500      
          
s = standard deviation =    100      
          
Thus,          
          
z = (x - u) / s =    -1.25   [ANSWER, Z SCORE]

**************************************  
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.25   ) =    0.894350226

Hence, 89.4350226% of students performed better than him. [ANSWER]

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