Homework Sourse36 Smokers According to the American Lung Association 90 of
36. Smokers: According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.
(a) Explain why this is a binomial experiment.
Answer:
(b) Find and interpret the probability that exactly 8 of them started smoking before 21 years of age.
(c) Find and interpret the probability that fewer than 8 of them started smoking before 21 years of age.
Answer:
(d) Find and interpret the probability that at least 8 of them started smoking before 21 years of age.
Answer
(e) Find and interpret the probability that between 7 and 9 of them, inclusive, started smoking before 21 years of age.
Answer:
| 36. Smokers: According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded. |
| (a) Explain why this is a binomial experiment. |
| Answer: |
| (b) Find and interpret the probability that exactly 8 of them started smoking before 21 years of age. |
| (c) Find and interpret the probability that fewer than 8 of them started smoking before 21 years of age. |
| Answer: |
| (d) Find and interpret the probability that at least 8 of them started smoking before 21 years of age. |
| Answer |
| (e) Find and interpret the probability that between 7 and 9 of them, inclusive, started smoking before 21 years of age. |
| Answer: |
Solution
36. Smokers: According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.
(a) Explain why this is a binomial experiment.
Answer: It is a binomial experiment because it has only 2 possible outcomes where one can be defined as the success and other can be defined as the failure. The probability of success and failure can be distinctly known
(b) Find and interpret the probability that exactly 8 of them started smoking before 21 years of age.
The required probability = 10C8 (0.9)8 (0.1)2 = 0.1937
(c) Find and interpret the probability that fewer than 8 of them started smoking before 21 years of age.
Answer:
P(X<8) = 1 - [ P(x=10) + P(x=9) + P(x=8) ]
= 1 - [ 0.19371 + 0.38742 + 0.34867]
= 1 - 0.9298 = 0.0702
This means 7.02% times less than 8 persons would have started smoking befiore 21 years of age.
(d) Find and interpret the probability that at least 8 of them started smoking before 21 years of age.
Answer
P(x=10) + P(x=9) + P(x=8) = probability of 8 or more people started before the age 21
= 0.19371 + 0.38742 + 0.34867
= 92.98% of the times, more than 8 people in a group of 10 would have started smoking before turning 21
(e) Find and interpret the probability that between 7 and 9 of them, inclusive, started smoking before 21 years of age.
Answer:
P ( 7 < X < 9 ) = P(x=7) + P(x=8) + P(x=9)
= 0.05739 + 0.19371 + 0.38742
= 0.5997
59.97 % chances are that there would be 7 to 9 people who would have started smoking before 21
| 36. Smokers: According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded. |
| (a) Explain why this is a binomial experiment. |
| Answer: It is a binomial experiment because it has only 2 possible outcomes where one can be defined as the success and other can be defined as the failure. The probability of success and failure can be distinctly known |
| (b) Find and interpret the probability that exactly 8 of them started smoking before 21 years of age. |
| The required probability = 10C8 (0.9)8 (0.1)2 = 0.1937 |
| (c) Find and interpret the probability that fewer than 8 of them started smoking before 21 years of age. |
| Answer: P(X<8) = 1 - [ P(x=10) + P(x=9) + P(x=8) ] = 1 - [ 0.19371 + 0.38742 + 0.34867] = 1 - 0.9298 = 0.0702 This means 7.02% times less than 8 persons would have started smoking befiore 21 years of age. |
| (d) Find and interpret the probability that at least 8 of them started smoking before 21 years of age. |
| Answer P(x=10) + P(x=9) + P(x=8) = probability of 8 or more people started before the age 21 = 0.19371 + 0.38742 + 0.34867 = 92.98% of the times, more than 8 people in a group of 10 would have started smoking before turning 21 |
| (e) Find and interpret the probability that between 7 and 9 of them, inclusive, started smoking before 21 years of age. |
| Answer: P ( 7 < X < 9 ) = P(x=7) + P(x=8) + P(x=9) = 0.05739 + 0.19371 + 0.38742 = 0.5997 59.97 % chances are that there would be 7 to 9 people who would have started smoking before 21 |
