A large corporation collected data on the reasons both middle managers and senior managers leave the company. Some managers eventually retire, but others leave the company prior to retirement for personal reasons including more attractive positions with other firms. Assume that the following matrix of one-year transition probabilities applies with the four states of the Markov process being retirement, leaves prior to retirement for personal reasons, stays as a middle manager, and stays as a senior manager.

	Retirement	LeavesPersonal	Middle Manager	Senior Manager
Retirement	1.00	0.00	0.00	0.00
LeavesPersonal	0.00	1.00	0.00	0.00
Middle Manager	0.02	0.08	0.75	0.15
Senior Manager	0.09	0.01	0.02	0.88

(a)

Which states are considered absorbing states? (Select all that apply.) Why?

RetirementLeaves-PersonalMiddle ManagerSenior Manager

A state is said to be absorbing if the probability of making a transition out of that state is 2 ---Select--- nonzero zero one , in this case, resulting in the manager 3 ---Select--- leaving remaining with the company.

(b)

Interpret the transition probabilities for the middle managers.

Probability of retiring=4Probability of leaving for personal reasons=5Probability of remaining a middle manager=6Probability of becoming a senior manager=7

(c)

Interpret the transition probabilities for the senior managers.

Probability of retiring=8Probability of leaving for personal reasons=9Probability of becoming a middle manager=10Probability of remaining a senior manager=11

(d)

What percentage of the current middle managers will eventually retire from the company? (Round your answer to one decimal place.)

What percentage of the current middle managers will leave the company for personal reasons? (Round your answer to one decimal place.)

(e)

The company currently has 920 managers: 630 middle managers and 290 senior managers. How many of these managers will eventually retire from the company? How many will leave the company for personal reasons? (Round your answers to the nearest integer.)

Number retiring?

Number leaving for personal reasons?