You can usually tell if you will solve a problem using sample proportions if the problem gives you a probability or percentage. For a sample proportion with probability p, the mean of our sampling distribution is equal to the probability. All formulas in this section can be found on page 2 of the given formula sheet.
However before you can solve the problem, you must first assure the sample is normally distributed by checking the large counts condition. The large counts condition assures that the number of success and failures is above 10 to be able to be normally distributed. The large counts condition is np ≥ 10 and n(1-p) ≥ 10
For the shape (normal) of distributions of means, you can check the Central Limit Theorem, but for proportions you must always check the Large Counts Condition.