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 smoking before 18 based on a random
sample of 200 adult smokers.
(b) interpret the mean.
(a) \\( \mu _ { x } = 140 \\)
\\( \sigma _ { x } = \square \\) (round to the nearest tenth as needed.)

Explanation:

Step1: Identify the parameters

This is a binomial distribution problem. Here, \(n = 200\) (sample size) and \(p=0.7\) (probability of success). The formula for the standard deviation of a binomial distribution is \(\sigma_{X}=\sqrt{np(1 - p)}\).

Step2: Substitute the values into the formula

Substitute \(n = 200\), \(p = 0.7\), and \(1-p=0.3\) into the formula \(\sigma_{X}=\sqrt{np(1 - p)}\).

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Step3: Calculate the value

\(\sqrt{42}\approx6.5\)

Answer:

\(6.5\)