Based on a study conducted by the Gallup organization, 76% of Americans believe that the state of moral values in the United States is getting worse. Suppose we obtain a simple random sample of n = 60 Americans and determine which believe that the state of the moral values in the United States is getting worse. Describe the sampling distribution of the sample proportion for Americans with this belief.

Approach If the sample size is less than 5% of the population size and np(1 – p) is at least 10, the sampling distribution of p̂ is approximately normal, with mean μ_p̂ = p and standard deviation

= p(1-p) n