Here is data on the flow of students through a school.

70% of freshmen pass and become sophomores, 20% fail and repeat as freshmen, 10% drop out

80% of sophomores pass and become juniors, 10% fail and repeat as sophomores, 10% drop out

80% of juniors pass and become seniors, 10% fail and repeat as juniors, 10% drop out

84% of seniors pass and graduate, 6% fail and repeat as seniors, 10% drop out

Treat this as a 6-state Markov chain with "graduated" and "dropped out" being absorbing states. Use an appropriate matrix tool to answer the following questions. (Give your answers correct to 3 decimal places.)

(a) What fraction of freshmen graduate within 4 years?

(b) What fraction of freshmen graduate within 5 years?

(c) What fraction of freshmen eventually graduate?

(d) What fraction of juniors eventually graduate?

(e) Assume that a student enters the school as a senior. What is the expected value for the number of years that person will spend in school before either graduating or dropping out?

years