A population of 10,000 is grouped as follows: 5000 nonsmokers, 2500 smokers of o
ID: 3440832 • Letter: A
Question
A population of 10,000 is grouped as follows: 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 7% probability that a nonsmoker will begin smoking a pack or less per day, and a 3% probability that a nonsmoker will begin smoking more than a 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 a 7% probability 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 and in 2 months? (Round your answers to the nearest whole number.)
(a) in 1 month
(b) in 2 months
nonsmokers= 1 pack/day or less= more than 1 pack/day =Explanation / Answer
a)
number of non smokers in 1 month
= 5000 - (7% + 3%) * 5000 + 10% * 2500 + 7% * 2500
= 4925
number of 1pack/day or less
= 2500 - (10% +10%) * 2500 + 7% * 5000 + 10% * 2500
= 2600
number of smokers who smoke more than 1 pack/day
= 10000 - 4925 - 2600
= 2475
b)
number of non smokers in 2 month
= 4925 - (7% + 3%) * 4925 + 10% * 2600 + 7% * 2475
= 4866
number of 1pack/day or less
= 2600 - (10% +10%) * 2600 + 7% * 4925 + 10% * 2475
= 2672
number of smokers who smoke more than 1 pack/day
= 10000 - 4866 - 2672
= 2462
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