Your first question you can solve using the Binomial distribution with X~Bin(12, 0.3). You are calculation the P(X>6) therefore, P(X=7)+P(X=8). . .P(X=12)=P(X>6).
For the second part, you are meant to understand the Binomial can be approximated using the Normal distribution with the mean equal to 1000(0.3) and standard deviation equal to the square root of 1000(0.3)(.07). Also, the p-value isn't needed here.