a) Try to use the CLT. You have to calculate $\displaystyle P(|\bar{X} - mu| \geq 6) $ using the change of variable $\displaystyle Z = (\bar{X} - \mu)/\var{\bar{X}}$
b) Since all the variables are independent,
$\displaystyle E(e^{t\sum_{k=1}^{36} X_k}) = E(e^{tX_1}) \dots E(e^{tX_{36}}) = \left(E(e^{tX_1})\right)^{36}$
and since you the distribution of X, you know the mgf.