Assume that 25% of students at a university wear contact lenses. We randomly pick 200 students. What is the probability that more than 28% of this sample wear contact lenses?
If 25% wear contacts then 28% of 200 is 56. The number of contact wearers in your sample has a binomial distribution B(200, 0.25).
Use the normal approximation to the binomial. So the mean of the normal is 50 and the standard deviation is sqrt(37.5) and you want to calculate the probability of observing value with a z-score greater than 6.5/sqrt(37.5).
CB