Chapter 7.6, Problem 40E

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.

1. 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.
2. b. What is the probability that the sample proportion will be within ±.03 of the population proportion?
3. c. Answer part (b) for a sample of 750 consumers.