In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, htere is an 8% propability that a nonsmoker will begin smoking a pack or less per day, and a 4% probablility that a nonsmoker will begin smoking more than one pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is an 8% probablity of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in a year? (Round your answers to the nearest whole number.) (a) i) in 1 month; ii) nonsmokers. (. )people iii) 1 pack/day or less (. )people more than 1 pack/day. (. )people (b) i) in 2 months ii) nonsmokers. (. )people iii) 1 pack/day or less. (. )people more than 1 pack/day (c) i) nonsmokers (. )people ii) 1 pack/day or less (. )people iii) more than 1 pack/day. (. )people
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, htere is an 8% propability that a nonsmoker will begin smoking a pack or less per day, and a 4% probablility that a nonsmoker will begin smoking more than one pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is an 8% probablity of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in a year? (Round your answers to the nearest whole number.)
(a)
i) in 1 month;
ii) nonsmokers. (. )people
iii) 1 pack/day or less (. )people
more than 1 pack/day. (. )people
(b)
i) in 2 months
ii) nonsmokers. (. )people
iii) 1 pack/day or less. (. )people
more than 1 pack/day
(c)
i) nonsmokers (. )people
ii) 1 pack/day or less (. )people
iii) more than 1 pack/day. (. )people
Here, we need to use transition matrix concept. Because, transition matrix is a matrix whose product with the initial or step gives state vector at a next or later time. In short it determine the trend with the help of transition matrix by using matrix multiplication. For this obtain the transition matrix and state vector .
| Non smokers | Smoking 1 pack or less per day | Smoking more than one pack per day | |
| Non smokers | 0.88 | 0.08 | 0.04 |
| Smoking 1 pack or less per day | 0.1 | 0.8 | 0.1 |
| Smoking more than one pack per day | 0.08 | 0.1 | 0.82 |
and
For a one month:
- Nonsmokers 4850 people.
- 1 pack/day or less 2650 people.
- More than 1 pack/day 2500 people.
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