Am I Normal?

Level 2

Bob recently took the Free Academic Koalification Exam (FAKE), in which one has to solve 5 math problems in the least amount of time. Bob completed the exam in about 84.25 84.25 seconds.

The mean time for all people taking the FAKE is 100 100 seconds, and the standard deviation is 10.5 10.5 seconds.

Assuming the times for the FAKE are approximately Normal distributed, which of the following is closest to the percent of people who completed the FAKE faster than Bob did?

(For your convenience, here is a z-score table ).

4 11 7 16

Sean Elliott by Sean Elliott , 21, USA

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1 solution

Sean Elliott
Jan 25, 2014

Bob's z-score is 84.25 − 100 10.5 = − 1.5 \frac{84.25-100}{10.5}=-1.5 . From the z-score table, this corresponds to an area of 0.0668 0.0668 , which is closest to 7 % \boxed{7\%} .

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