Question

According to ”research” 90 % of adult cigarette smokers started smoking before the age of 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.) What random variable models the number of smokers who began smoking before the age of 21 in the random sample of 21 adult smokers? b.) Write down the probability mass function for your answer in a.) c.) What is the probability fewer than 9 smokers started smoking before the age of 21? d.) What is the expected value of smokers who began smoking before the age of 21 in this experiment? e.) What is the variance in this experiment?

Answer 1

a) This is Binomial distribution because we have probability of success p = 0.9 given, number of trials n = 10 is finite, and output of each trail is independent of each other. Hence this is Binomial random variable.

This is the answer.

So, the probability fewer than 9 smokers started smoking before the age of 21 is 0.2639.

d) E(x) = mean = n*p = 10*0.9 = 9

So, expected value is 9.

e) Variance = n*p*q = 10*0.9*0.1 = 0.9

So, variance is 0.9.

Please comment if any doubt. Thank you.