At the school, it is typical for some fraction of students to pass an certification exam. Recently, funding was used to develop a new program that was designed to increase the proportion of students who pass the exam. The school that developed this program studied 475 students and found that the percentage of students who passed the certification increased to 72% with a 95% confidence interval of [.68, .76]. One of analysts conducted a hypothesis test, H0: No improvement / same rate as always vs. H1: The intervention changed the passing rate, and the null hypothesis was rejected with a p-value of .045. That analyst left the firm, and the data are not available, but Mark needs to understand exactly what these results mean.

• What is the probability that the true passing rate of the new exam is above 75%?