I am not understanding this last portion of my statistics class. I am completely confused about critical values. Please help me. Thank you!!

What critical value for z would be used to test the hypotheses: H_0:μ≥15 and H_a:μ<15, for a = 0.01 ?

You have a one-tailed test. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.01) for your Z score.