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A Challenging National Math Contest - Normally Distributed Scores

APSTAT-XQ1JEL

The AMC-12A is national math contest which is known to be very challenging. Statistics made available to the public show that the mean score on this contest in 2015 was $69.90$ and the standard deviation was $20.21$. A total of $55,833$ students participated and the distribution of scores was approximately normal.

Approximately what proportion of students who participated in the AMC-12A in 2015 had scores below $50$?

A

Approximately $0$

B

$0.162$

C

$0.285$

D

$0.715$

E

$0.838$