Question

According to an​ almanac,

70% of adult smokers started smoking before turning 18 years old.

​(a) If 300 adult smokers are randomly​ selected, how many would we expect to have started smoking before turning 18 years​ old?

​(b) Would it be unusual to observe 255 smokers who started smoking before turning 18 years old in a random sample of 300

adult​ smokers? Why?

Answer 1

Let X = Number of smokers out of 300 who started smoking before turing 18.
Then X~Binomial(300,70%)
=> X~Binomial(300,0.7)

a. Now, by using the properties of binomial distribution, expected number of smokers who started smoking before turning 18 = E(X)= 300x0.7
=> E(X) = 210

b.

So, putting the values in the formula, we get

P(X=225) = 0.008 = 0.8%

So, yes it would be unusual to observe 255 smokers who started smoking before turning 18 years old in a random sample of 300 because probability of that happening is very low, i.e. 0.8%(which is less than 5%)

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