Question 1187156
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During the scholarship examination of a certain scholarship grant taken by 10,000 applicants, 
Donnabelle's score was 350 greater than the scores of 8995 applicants who took the examination. 
What is the percentile of Donnabelle's score?
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The solution in the post by  @CPhill is  INCORRECT.



In his solution,  @CPhill states


    2. **Applicants scoring the same or higher:** Since there were 10,000 applicants total, 
    the number of applicants who scored the same or higher than Donnabelle is 10,000 - 8995 = 1005.



It is incorrect.    From the problem,  we  CAN  NOT  conclude it.


From the problem,  we know that Donnabelle' score was  350 greater than the scores of  8995  applicants;
but we can not conclude that the number of applicants who scored the same or higher than  Donnabelle 
is   10,000 - 8995 = 1005.



        The statement,  which  @CPhill makes at this point,  is a logical mistake.



Based on the information given in the post, it is NOT POSSIBLE to determine the Donnabelle' percentile precisely;
we only may get an  {{{highlight(highlight(estimation))}}}  that the Donnabelle' percentile is at least


            {{{((10000-8995)/10000)*100}}} = 89.95.



The given info,  related to the concrete value of  350  scores, 

does not work in the problem and  (in the given context)  can not be used in the solution.