The National Collegiate Athletic Association (NCAA) has a public access database on each Division I sports team in the United States, which contains data on team-level Academic Progress Rates (APRs), eligibility rates, and retention rates. The mean APR of 359 men's basketball teams for the 2010-2011 academic year was 950.35 (based on a 1,000-point scale), with a standard deviation of 30.58. Assuming that the distribution of APRs for the teams is approximately normal,
a. Would a team be at the upper quartile (the top 25%) of the APR distribution with an APR score of975?
b. What APR score should a team have to be more successful than 75% of all the teams?
c. What is the Z value for this score?