Answered: Here is data on the flow of students…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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
82% of seniors pass and graduate, 8% 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

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