The UCSB BARC office knows that in any given quarter, of the 11,200 undergraduate students in their first or second year, 15% of them will have an outstanding balance at the start of the quarter.

a. (5 points) If we let X be the number of students with an outstanding balance, and assume that the students' accounts are independent, state the distribution of X and verify by checking any relevant criteria.

b. (3 points) What is an appropriate distribution to approximate the distribution of X (include the parameter value(s))? Verify any relevant criteria.

c. (5 points) What is the probability that more than 1,742 students will have an outstanding balance at the start of any given quarter? (Use the approximate distribution from part (b).)