I have the equation $$\Pr(X\le6)=\sum_{x=6}^{∞}\left({e^{-4.8}}\cdot\frac{4.8^{x}}{x!}\right).$$
And it is not equating to when I sum each term manually.
Plugging this into my calculator I get 0.348994, however when I sum each term (like below) I get 0.790805 which seems more likely.
$$\Pr(X\le6)=\Pr(X=0)+\Pr(X=1)+\Pr(X=2)+\Pr(X=3)+\Pr(X=4)+\Pr(X=5)+\Pr(X=6)\\=\left({e^{-4.8}}\cdot\frac{4.8^{0}}{0!}\right)+\left({e^{-4.8}}\cdot\frac{4.8^{1}}{1!}\right)+\left({e^{-4.8}}\cdot\frac{4.8^{2}}{2!}\right)+\left({e^{-4.8}}\cdot\frac{4.8^{3}}{3!}\right)+\left({e^{-4.8}}\cdot\frac{4.8^{4}}{4!}\right)+\left({e^{-4.8}}\cdot\frac{4.8^{5}}{5!}\right)+\left({e^{-4.8}}\cdot\frac{4.8^{6}}{6!}\right)$$ $$=0.00823+0.39503+0.94807+0.151691+0.182029+0.174748+0.139798$$ $$=0.790805$$
I have been through my working several times now and don't know where I went wrong...
The sum goes from $x=0$ to $6$, not $6$ to $\infty$.