Normal approximation for a sample proportion. A sample survey contacted an SRS of 700 registered voters in Oregon shortly after an election and asked respondents whether they had voted. Voter records show that 56% of registered voters had actually voted. We will see in the next chapter that in this situation the proportion ^p of the sample who voted has approximately the Normal distribution with mean μ = 0.56 and standard deviation σ = 0.019
(a) If the respondents answer truthfully, what is P(0.52 ≤P^≤ 0.60)? This is the probability that the statistic P^ estimates the parameter 0.56 within plus or minus 0.04.
(b) In fact, 72% of the respondents said they had voted (P^ = 0.72). If respondents answer truthfully, what is P(P^ ≥ 0.72)? This probability is so small that it is good evidence that some people who did not vote claimed that they did vote.