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Free-response questions on the AP Calculus Exam are scored $0$ through $9$. A question on one of the previous exams had an average score of $3.10$ with a standard deviation of $2.45$.

What was the approximate score achieved by a student that would put him or her in the $87$th percentile on this question?

You may assume the scores on this question are approximately normally distributed.

A

$0.34$

B

$0.97$

C

$1.74$

D

$5.23$

E

$5.86$

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