This is a reasonable answer, however, it is not correct. Recall the probability that we obtain a sample mean as large as or greater than 580 with a sample of n = 10, given that the population mean is 555 is .2843. This means that 28% of the time when we take a sample of 10 people from a population with a mean of 555, the sample mean would be 580 or above.
The most important issue to understand here is that a sample mean as large as 580 is quite likely even if the population mean is 555. Since the sample mean is likely to be as large as 580 by chance, we cannot claim with confidence that the program graduates score better than 555 on average.
More -- When would we be able to conclude that the program raises GRE scores?