A USA Today poll asked a random sample of 1012 U.S. adults what they do with the milk in the bowl after they have eaten the cereal. Let p^ be the proportion of people in the sample who drink the cereal milk. A spokesman for the dairy industry claims that 70% of all U.S. adults drink the cereal milk. Suppose this claim is true.

a. What is the mean of the sampling distribution of p̂?

b. Find the standard deviation of the sampling distribution of p̂. Verify that the 10% condition is met.

c. Verify that the sampling distribution of p̂ is approximately Normal.

d. Of the poll respondents, 67% said that they drink the cereal milk. Find the probability of obtaining a sample of 1012 adults in which 67% or fewer say they drink the cereal milk, assuming the milk industry spokesman’s claim is true.

e. Does this poll give convincing evidence against the spokesman’s claim? Explain your reasoning.