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Probability that the sum of all values of 5 pairs of dice will be between 30 and 40

Roll 10 dice. What is the probability the average is between 3 and 4?

I know E[x] = 3.5 for one roll and one would the same for n rolls. I am having difficulty wrapping my head around finding the probability for between the two rolls though.

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    I don't quite know how you are *intended* to do this. (And additional point: it is not clear whether exactly $3$ or $4$ are meant to be included.) One **could** use the normal approximation, but $10$ is on the small side for reliability of the approximation.2012-11-15
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    Repeat: http://math.stackexchange.com/questions/236849/probability-that-the-sum-of-all-values-of-5-pairs-of-dice-will-be-between-30-and2012-11-15

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