Problem
This question: 1 point(S) possible Submit According to an almanac, $80 \%$ 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 300 adults. (b) Interpret the mean. (a) $\mu_{x}=\square$ $\sigma_{\mathrm{x}}=\square$ (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 300 adult smokers, 240 will have started smoking before turning 18. B. It is expected that in a random sample of 300 adult smokers, 240 will have started smoking after turning 18. C. It is expected that in $50 \%$ of random samples of 300 adult smokers, 240 will have started smoking before turning 18 Submi
Solution
Step 1 ：Step 1: Understand the problem.
Step 2 ：Step 2: Calculate the mean using the formula \(\mu_x = n \cdot p\), where \(n = 300\) and \(p = 0.8\).
Step 3 ：Step 3: Calculate the standard deviation using the formula \(\sigma_x = \sqrt{n \cdot p \cdot (1 - p)}\), where \(n = 300\) and \(p = 0.8\).
Step 4 ：Step 4: Interpret the mean as follows: A. It is expected that in a random sample of 300 adult smokers, 240 will have started smoking before turning 18.
Step 5 ：The mean is \(\boxed{240}\) and the standard deviation is \(\boxed{6.9}\) (rounded to the nearest tenth).
