In 2016 Americans owed $1.3 trillion in student loans. The default rates of college student loans determine eligibility for colleges to receive federal student aid. According to the Department of Education, an average of 11.5% of Americans who had student loans defaulted on their loans. A random sample of 210 recent graduates was randomly selected.

a. What is the probability that 10% or less of this sample has defaulted on their student loans?

b. What is the probability that 15% or more of this sample has defaulted on their student loans?

c. What is the probability that between 10% and 20% of this sample has defaulted on their student loans?

d. Suppose that 30 students from this sample defaulted on their student loans. Does this result support the claim made by the Department of Education?