4.Question Details LarLinAlg8 2.5.015. [3777430] In a population of 10,000, ther

Question

4.Question Details LarLinAlg8 2.5.015. [3777430] 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, there is a 9% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% 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 6% 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, in 2 months, and in 1 year? (Round your answers to the nearest whole number.) (a) in 1 month nonsmokers 1 pack/day or less 2 more than 1 pack/day 4750 people 2700 people 2550 people (b) in 2 months 4556people 1 pack/day or less 2843 people more than 1 pack/day 2602 people (c) in 1 year nonsmokers 1 pack/day or less more than 1 pack/day 3907 people |-3190 | people 2903 people |

Explanation / Answer

Total persons=10,000

At the beginning of 1st month,

Number of non smoker=5000

Number of people who smoke 1pack or less per day =2500

Number of people who smoke more that 1 pack per day =2500

a) At the end of Ist month,

Number of non-smoker= 5000 x 0.87 + 2500 x 0.1 + 2500 x 0.06

=4350+250+150=4750

Number of people who smoke 1 pack or less per day = 5000 x 0.09 + 2500 x 0.8 + 2500 x 0.1

=450 + 2000 + 250 = 2700

Number of people who smoke more than 1 pack per day = 5000 x 0.04 + 2500 x 0.1 + 2500 x 0.84

= 200 + 250 + 2100 = 2550

b)At the end of second month

Number of non smoker = 4750 x 0.87 + 2700 x 0.1 + 2550 x 0.06

= 4132.50 + 270 + 153 ( rounding to nearest whole no)

= 4133 + 270 + 153 = 4556

Number of people who smoke 1 pack or less per day = 4750 x 0.09 + 2700 x 0.8 + 2550 x 0.1

= 427.50 + 2160 + 255 ( rounding to nearest whole no)

= 428 + 2160 + 255 = 2843

Number of people who smoke more than 1 pack per day = 4750 x 0.04 + 2700 x 0.1 + 2550 x 0.84

= 190 +270 + 2142 = 2602

c)At the end of 3rd month

Number of non smoker= 4556 x 0.87 + 2843 x 0.1 + 2602 x 0.06

=3963.72 + 284.3 + 156.12 (rounding to nearest whole no)

= 3964 + 284 + 156 = 4404

Number of people who smoke 1pack or less per day = 4556 x 0.09 + 2843 x 0.8 + 2602 x 0.1

= 410.04 +2274.4 + 260.2

= 410 + 2274 + 260 = 2944

Number of people who smoke more than 1 pack per day = 4556 x 0.04 + 2843 x 0.1 + 2602 x 0.84

= 182.24 + 284.3 + 2185.68 (rounding to nearest whole no)

= 182 + 284 + 2186

= 2652

Continuing in this way , we can find number of people who are non smoker,smoke 1 pack or less per day,smoke more than one pack per day at the end of 12 months i.e at end of 1 year.

PROBABILITY TABLE begin smoking 1 pack or less per day begin smoking 1 pack or more per day be non smoker Probability that a non smoker will 9%=0.09 4%=0.04 (100-(9+4))%=87%=0.87 Probability that a smoker who smoke 1 pack or less per day will (100-(10+10))%=80%=0.8 10%=0.1 10%=0.1 Probability that a smoker who smoke more than 1 pack per day will 10%=0.1 (100-(10+6))%=84%=0.84 6%=0.06

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.