Two large high schools in a city (3000 students in each school) claim they have a higher rate of students who go on to graduate from a 4-year university. 57% of students from school A go on to graduate from a 4 year university and 61% from school B. A random sample of 75 students from school A and 80 from school B are selected and followed to determine if they graduate from a 4-year university.

a. Find the probability that difference in sample proportions is more than 6.

b. What is the probability that School A sample proportion is more than 5% higher than School B?