The Food Marketing Institute shows that 17% of households spend more than $100per week on groceries. Assume the population proportion is p=.17and a simple random sample of 800800 households will be selected from the population.

a. Show the sampling distribution of p¯, the sample proportion of households spending more than $100per week on groceries.

b. What is the probability that the sample proportion will be within ±.02of the population proportion?

c. Answer part (b) for a sample of 1600households.