Question

According to an​ almanac, 70​% of adult smokers started smoking before turning 18 years old. ​

(a) Compute the mean and standard deviation of the random variable​ X, the number of smokers who started before 18 in 300 trials of the probability experiment.

​(b) Interpret the mean.

​(c) Would it be unusual to observe 240 smokers who started smoking before turning 18 years old in a random sample of 300 adult​ smokers? Why?

Answer 1

a) n = 300

    p = 0.7

= n * p = 300 * 0.7 = 210

= sqrt(np(1 - p))

   = sqrt(300 * 0.7 * 0.3) = 7.9373

b) Out of 300 adult smokers the average number of smokers who have started smoking before turning 18 years old is 210.

c) P(X = 240)

= P((239.5 - )/< (X - )/< (240.5 - )/)

= P((239.5 - 210)/7.9373 < Z < (240.5 - 210)/7.9373)

= P(3.72 < Z < 3.84)

= P(Z < 3.84) - P(Z < 3.72)

= 1 - 1 = 0

Since the probability value is less than 0.05, so it would be unusual to observe 240 smokers.