Answer: C) 40th percentile
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Step-by-step explanation:
The original list is {827,691,616,740,651,772,868,557,891,937} which has 10 items inside it.
The list sorts to {557,616,651,691,740,772,827,868,891,937}
We see that there are 3 items below 691. So one way to calculate the percentile is to do 3/10 = 30% like you did for your answer.
However, the term "percentile" is ambiguous as there is another way to calculate percentile. The other method involves the term in question. So we have 4 terms in the sublist {557,616,651,691} which is how your friend got 4/10 = 40%
It's unfortunate why this term is not well defined. Ideally your teacher would state instructions on how to deal with this dilemma, or post a formula to use.
The good news is at least "30th percentile" isn't listed as an answer choice, so we can rule out the first method above.