Sampling. Suppose that the proportion of all adult Americans who rate economic conditions in the United States as poor is p = 0.37.

This number is consistent with a Gallup Poll conducted from February 25 to March 1, 2008. If we took many SRSs of size 3500 (the sample size used by the Gallup Poll), the sample proportion ^p would vary from sample to sample following a Normal distribution with mean 0.37 and standard deviation 0.01. Use this fact and the 68–95–99.7 rule to answer these questions.

(a) In many samples, what percentage of the values of ^p fall above 0.37? Above 0.40?

(b) In a large number of samples, what range contains the central 95% of values of ^p?