Hey Lostinstats.

Hint: The distribution of (mu - mu_hat)/sigma ~ N(0,1) given that you have a population Normal(mu,sigma^2) = Normal(75,25). Re-arrange to get the distribution of mu_hat and then solve for that probability.

Hint: for (b) do the same thing except look at the chi-square distribution where (n-1)S^2/sigma^2 ~ Chi-Square(n-1).