1. Are Americans interested in opinion polls about the major issues of the day?

Are the correct probabilities 68% for 1a. and 95% for 1b. ?

1. Are Americans interested in opinion polls about the major issues of the day? Suppose that 40% of all adults are veryinterested in such polls. (According to sample surveys that ask this question, 40% is about right.) A polling firm chooses anSRS of 1015 people. If they do this many times, the percentage of the sample who say they are very interested will varyfrom sample to sample following a Normal distribution with mean 40% and standard deviation 1.5%. Use the 68—95—997 rule to answer these questions. (a) What is the probability that one such sample gives a result within 11.5% of the truth about the population? (b) What is the probability that one such sample gives a result within i3% of the truth about the population?