Question

statistics question about smoking before 18 years of age

According to an almanac, 70% of adult smokers started smoking before turning 18 years oh When technology is used, use the Tech Help button for further assistance. 

(a) Compute the mean and standard deviation of the random variable X, the number of smokers who started before 18 in 100 trials of the probability experiment 

(b) Interpret the mean.

(c) Would it be unusual to observe 80 smokers who started smoking before turning 18 years old in a random sample of 100 adult smokers? Why? (a) Mu x =0.18 Sigma x= D (Round to the nearest tenth as needed.) 

(b) What is the correct interpretation of the mean? 

A. It is expected that in a random sample of 100 adult smokers, 70 will have started smoking after turning 18. 

B. It is expected that in a random sample of 100 adult smokers, 70 will have started smoking before turning 18 

C. It is expected that in 50% of random samples of 100 adult smokers, 70 will have started smoking before turning 18.

 (c) Would ft be unusual to observe 80 smokers who started smoking before turning 18 years old in a random sample of 100 adult smokers? 

A. No, because 80 is less than \(\mu-2 \sigma\).

B. Yes, because 80 is between \(\mu-2 \sigma\) and \(\mu+2 \sigma\).

C. Yes, because 80 is greater than \(\mu+2 \sigma\).

D. No, because 80 is between \(\mu-2 \sigma\) and \(\mu+2 \sigma\).

E. No, because 80 is greater than \(\mu+2 \sigma\).

Answer 1

Note: Since we are counting the number of "successes" (# who started smoking BEFORE 18) in n independent trials with a constant probability,X has a binomial distribution with parameters n 100 and p .70 Note: The following notation varies from book-to-book. 100(. 70-70 Ах пр ox Vn p (1-p) /100 .70. (1 -.30) 4.6 Answer: B Note: The mean of a binomial equals the expected value. So, if we sample 100 people, we "expect" 100(.70) 70 people to start smoking before the age of 18 years old Note: An observation is considered unusual if tis MORE than 2 standard deviation away from the mean, Le. u t2o 70 t 2(4.6(60.8,79.2) So, any number between 61 and 79 would NOT be considered unusual. So, any number 60 or less, or 80 or more is considered unusual Answer: C I hope this helps. If you have any questions, please ask them in the comment section. :)