EXAMPLE 4 Do you approve of gambling?

An opinion poll asks an SRS of 501 teens, “Generally speaking, do you approve or disapprove of legal gambling or betting?” Suppose that, in fact, exactly 50% of all teens would say Yes if asked. (This is close to what polls show to be true.) The poll’s statisticians tell us that the sample proportion who say Yes will vary in repeated samples according to a Normal distribution with mean 0.5 and standard deviation about 0.022. This is the sampling distribution of the sample proportion .

The 68–95–99.7 rule says that the probability is 0.16 that the poll gets a sample in which fewer than 47.8% say Yes. Figure 18.3 shows how to get this result from the Normal curve of the sampling distribution.