so the question is basically asking you to set x-b(n,0.2) where you have to find the greatest value for n that gives you a probability of >0.9 for seeing all patients that turn up. so you have to increase n 1 by 1 until you hit a probability which is just smaller than 0.9 where that number before, which would should be greater than 0.9, is your answer, also known as the 'critical value' (i think).
Tell me if you need any more help, or if I've explained it poorly
Im also learning stats myself