Question

III.16. Worrying about crime. How much do Americans worry about crime and violence? Suppose that 40% of all adults worry a great deal about crime and violence. (According to sample surveys that ask this question, 40% is about right.) A polling firm chooses an SRS of 2400 people. If they do this many times, the percentage of the sample who say they worry a great deal will vary from sample to sample following a Normal distribution with mean 40% and standard deviation 1.0%. Use the 68–95–99.7 rule to answer these questions.

  1. (a) What is the probability that one such sample gives a result within ±1.0% of the truth about the population?

  2. (b) What is the probability that one such sample gives a result within ±2% of the truth about the population?