Let's do some back of the envelope calculations.
We have 30 samples, and the std of each sample is known. So the std of the mean is going to be $5 / \sqrt(30) \approx 1\% $
so, roughly applying the central limit theorem (be careful when applying the CLT ! it's full of traps ! learn about them), the distribution of the mean of the 30 samples is going to be a Gaussian, of std 1%, centered around $\mu_a$
Seeing a value that close to 65% for the realization of that variable, it's quite likely that the hypothesis that $\mu_a \geq 65$ is wrong
For the second part, we want to compute the probability of the difference of two Gaussians of std 1% to be bigger than 5.5. Very roughly, the difference of the two Gaussians will have std $\approx\sqrt(2)\approx1.5$ so that 5.5 is between 3 and 4 stds of deviation. That's a pretty good separation and is strong evidence for $\mu_a \neq \mu_b$
Now that I've done the back of the enveloppe calculations, try to redo all of this more rigorously