According to an almanac, $80 \%$ 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? (a) We would expect about 240 adult smokers to have started smoking before turning 18 years old (Type a whole number.) (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? A. Yes, because 255 is greater than $\mu+2 \sigma$. B. Yes, because 255 is between $\mu-2 \sigma$ and $\mu+2 \sigma$. C. No, because 255 is less than $\mu-2 \sigma$ D. No, because 255 is greater than $\mu+2 \sigma$ E. No, because 255 is between $\mu-2 \sigma$ and $\mu+2 \sigma$.

Step 1 ：Given that 80% of adult smokers started smoking before turning 18 years old, we can calculate the expected number of adult smokers who started smoking before 18 by multiplying the total number of adult smokers by the percentage of smokers who started before 18. In this case, the total number of adult smokers is 300 and the percentage is 80% or 0.8. Therefore, the expected number of adult smokers who started smoking before 18 is \(300 \times 0.8 = 240\).

Step 2 ：To determine whether it would be unusual to observe 255 smokers who started smoking before turning 18 years old in a random sample of 300 adult smokers, we need to calculate the standard deviation and compare the observed value to the mean and standard deviation.

Step 3 ：The standard deviation is approximately 6.93. The z-score for 255 smokers is approximately 2.17. A z-score of 2.17 means that 255 smokers is 2.17 standard deviations above the mean.

Step 4 ：In a normal distribution, about 95% of the data falls within 2 standard deviations of the mean. Therefore, observing 255 smokers who started smoking before 18 is unusual because it falls outside of the range of what we would expect 95% of the time.

Step 5 ：Final Answer: (a) We would expect \(\boxed{240}\) adult smokers to have started smoking before turning 18 years old. (b) Yes, because 255 is greater than \(\mu+2 \sigma\).