Travel agent training. A chain of travel agencies maintains a training program for new travel agents. Initially, all new employees are classified as beginning agents requiring extensive supervision. Every 6 months, the performance of each agent is reviewed. Past records indicate that after each semiannual review, 40 % of the beginning agents are promoted to intermediate agents requiring only minimal supervision. 10 % are terminated for unsatisfactory performance, and the remainder continue as beginning agents. Furthermore, 30 % of the intermediate agents are promoted to qualified travel agents requiring no supervision. 10 % are terminated for unsatisfactory performance, and the remainder continue as intermediate agents. (A) Draw a transition diagram. (B) Write the transition matrix. (C) What is the probability that a beginning agent is promoted to qualified agent within 1 year? Within 2 years?
Travel agent training. A chain of travel agencies maintains a training program for new travel agents. Initially, all new employees are classified as beginning agents requiring extensive supervision. Every 6 months, the performance of each agent is reviewed. Past records indicate that after each semiannual review, 40 % of the beginning agents are promoted to intermediate agents requiring only minimal supervision. 10 % are terminated for unsatisfactory performance, and the remainder continue as beginning agents. Furthermore, 30 % of the intermediate agents are promoted to qualified travel agents requiring no supervision. 10 % are terminated for unsatisfactory performance, and the remainder continue as intermediate agents. (A) Draw a transition diagram. (B) Write the transition matrix. (C) What is the probability that a beginning agent is promoted to qualified agent within 1 year? Within 2 years?
Solution Summary: The author illustrates the transition diagram when a travel agency's semiannual review indicates that 40% of the beginning agents are promoted to intermediate agents, 102% are terminated for unsatisfactory performance
Travel agent training. A chain of travel agencies maintains a training program for new travel agents. Initially, all new employees are classified as beginning agents requiring extensive supervision. Every
6
months, the performance of each agent is reviewed. Past records indicate that after each semiannual review,
40
%
of the beginning agents are promoted to intermediate agents requiring only minimal supervision.
10
%
are terminated for unsatisfactory performance, and the remainder continue as beginning agents. Furthermore,
30
%
of the intermediate agents are promoted to qualified travel agents requiring no supervision.
10
%
are terminated for unsatisfactory performance, and the remainder continue as intermediate agents.
(A) Draw a transition diagram.
(B) Write the transition matrix.
(C) What is the probability that a beginning agent is promoted to qualified agent within
1
year? Within
2
years?
The National Center for Health Statistics, housed within the U.S. Centers for Disease Control and Prevention (CDC), tracks the number of adults in the United States who have health insurance. According to this agency, the uninsured rates for Americans in 2018 are as follows: 5.1% of those under the age of 18, 12.4% of those ages 18-64, and 1.1% of those 65and older do not have health insurance (CDC website). Approximately 22.8% of Americans are under age 18, and 61.4% of Americans are aged 18-64. Given that the person is an uninsured American, what is the probability that the person is 65 or older (to 3 decimals)?
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Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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