Recall the use of data from the National Health Survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U.S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16.

Prompt
Suppose that we randomly select 100 U.S. adults who are smokers and find that 25% of this sample started smoking before the age of 16. Is this much error surprising? Find the probability that a sample proportion will be an over- or underestimate of the parameter by more than 5%.

Show your work by checking normality conditions, calculating a z-score, explaining how the area under the normal curve is used to answer the question, and stating a conclusion in the context of this problem.