Data for the progression of college students at a St. Joseph College are summarized in the following matrix of transition probabilities: States Graduate Drop out Freshman Sophomore Junior Senior Graduate 1 0 0 0 0 0 Drop out 0 1 0 0 0 0 Freshman 0 0.15 0.10 0.75 0 0 Sophomore 0 0.15 0 0.05 0.80 0 Junior 0 0.10 0 0 0.10 0.8 Senior 0.8 0.05 0 0 0 0.15 a. In an address to the incoming class of 600 freshmen, the dean asks the students to look around the auditorium and realize that about 50% of the freshmen present today will not make it to graduation day. Does your Markov process analysis support the dean’s statement? Explain. b. Currently, the college has 600 freshmen, 520 sophomores, 460 juniors, and 420 seniors. What percentage of the 2000 students attending the college will eventually graduate?
Data for the progression of college students at a St. Joseph College are summarized in the following matrix of transition probabilities: States Graduate Drop out Freshman Sophomore Junior Senior Graduate 1 0 0 0 0 0 Drop out 0 1 0 0 0 0 Freshman 0 0.15 0.10 0.75 0 0 Sophomore 0 0.15 0 0.05 0.80 0 Junior 0 0.10 0 0 0.10 0.8 Senior 0.8 0.05 0 0 0 0.15 a. In an address to the incoming class of 600 freshmen, the dean asks the students to look around the auditorium and realize that about 50% of the freshmen present today will not make it to graduation day. Does your Markov process analysis support the dean’s statement? Explain. b. Currently, the college has 600 freshmen, 520 sophomores, 460 juniors, and 420 seniors. What percentage of the 2000 students attending the college will eventually graduate?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 42E
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Data for the progression of college students at a St. Joseph College are summarized in the following matrix of transition
| States | Graduate | Drop out | Freshman | Sophomore | Junior | Senior |
|
Graduate |
1 | 0 | 0 | 0 | 0 | 0 |
| Drop out | 0 | 1 | 0 | 0 | 0 | 0 |
| Freshman | 0 | 0.15 | 0.10 | 0.75 | 0 | 0 |
| Sophomore | 0 | 0.15 | 0 | 0.05 | 0.80 | 0 |
| Junior | 0 | 0.10 | 0 | 0 | 0.10 | 0.8 |
| Senior | 0.8 | 0.05 | 0 | 0 | 0 | 0.15 |
a. In an address to the incoming class of 600 freshmen, the dean asks the students to look around the auditorium and realize that about 50% of the freshmen present today will not make it to graduation day. Does your Markov process analysis support the dean’s statement? Explain.
b. Currently, the college has 600 freshmen, 520 sophomores, 460 juniors, and 420 seniors. What percentage of the 2000 students attending the college will eventually graduate?
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