The gpa at the super university has a normal distribution with a mean 2.29 and standard deviation 1.29 to be an honors student at this university your gpa has to be in the top 20% what is the smallest gpa you need to have to be an honors student?

The smallest GPA needed to fall in the top 20% is , where



where is a random variable denoting GPA scores. Transform to the standard normal random variable using



where and are the mean and standard deviation of , respectively. Now



Using the inverse CDF for the standard normal distribution, we find that the corresponding critical value is about 0.8416, which means

21 is the answer the answer is 21