SOLUTION: 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 exa

Question 1187156: 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?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1987)   (Show Source): You can put this solution on YOUR website!
Here's how to determine Donnabelle's percentile:
1. **Applicants scoring lower:** Donnabelle scored higher than 8995 applicants.
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.
3. **Percentile calculation:** Percentile is calculated as (number of scores below a given score / total number of scores) * 100. In Donnabelle's case, the number of scores below hers is 8995.
Percentile = (8995 / 10000) * 100 = 89.95
Therefore, Donnabelle's score is at the 89.95th percentile.

Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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 that the Donnabelle' percentile is at least

         = 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.

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