Question: We like opinion polls. Are Americans interested in opinion polls about the major issues of the day? Suppose that 40% of all adults are very interested in such polls. (According to sample surveys that ask this question, 40% is about right.) A polling firm chooses an SRS of 1015 people. If they do this many times, the percentage of the sample who say they are very interested will vary from sample to sample following a Normal distribution with mean 40% and standard deviation 1.5%. Use the 68-95-99.7 rule to answer these questions.
(a) What is the probability that one such sample gives a result within ±1.5% of the truth about the population?
(b) What is the probability that one such sample gives a result within ±3% of the truth about the population?