Finding probability using Central Limit Theorem


so today I had an probability/statistics exam and there was a problem that lot of people, including me, were struggling with.
Here's the problem: 300 numbers, rounded to 1 decimal place, were summed up. Using the Central Limit Theorem find out what is the probability, that the absolute value of the error of the sum, which is caused by rounding, isn't bigger than 1.

I tried creating the "formula", which would help me solve this by writing up something like P(|summing up error| <= 1) ... P (-1 <= summing up error <= 1) but i just couldn't find a way to get the mu and sigma value.

If anyone could help me with this, it would be greatly appreciated.
Also sorry for the english.


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For one of those numbers (call it X) what would you use to model the difference between X and the rounded version of X?