I'm trying to solve a question that asks:
If 5 pairs of fair dice are rolled, approximate the probability that the sum of the values obtained is between 30 and 40 inclusive.
My approach so far, was to create a random variable called $T$ whose range is from $10$ to $60$ and look for $P\{|T-35| \le 5\} $
I don't know what to do next. Can I proceed like this is a normal distribution or is five too small a sample to qualify for the Central Limit Theorem?