Chapter 7.6, Problem 36E

The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product's label. Assume the population proportion is $p=.76$ and a sample of 400 consumers is selected from the population.
a. Show the sampling distribution of the sample proportion $\bar{p}$ , where $\bar{p}$ is the proportion of the sampled consumers who read the ingredients listed on a product's label.
b. What is the probability that the sample proportion will be within $\pm .03$ of the population proportion?
c. Answer part (b) for a sample of 750 consumers.