Calculate that the difference between two teams will be in interval $[5,9]$

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We know these facts: the mean of score difference between two teams is $3.5$. The team with probability $p_1=0.5$ will win by $4,5,6$ or more points and with $p_2=0.5$ will win by $0,1,2,3$ or lose by any result. How to calculate that the difference between two teams will be in interval $[5,9]$? I think we need to use Poisson distribution because then, $variance=mean$ but I don't know how to correctly write it.