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 see in the next chapter that in this situation the proportion of the sample p⁄

who voted has approximately the Normal distribution with mean m 5 0.56 and standard deviation s 5 0.019.

(a) If the respondents answer truthfully, what is Ps0.52 #p⁄

# 0.60d? This is the probability that the sample proportion p⁄

estimates the mean of 0.56 within plus or minus 0.04.

(b) In fact, 72% of the respondents said they had voted

(p⁄

5 0.72). If respondents answer truthfully, what is Psp⁄

$ 0.72d? This probability is so small that it is good evidence that some people who did not vote claimed that they did vote.