Solve this: Drinking the cereal milkSolve this:

Drinking the cereal milk? A USA Today poll asked a random sample of 1012 U.S. adults what they do
with the milk in their cereal bowl after they have eaten. Let § 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): Calculate the mean and standard deviation of the sampling distribution of f. Interpret the standard deviation.
(b): Justify that the sampling distribution of $ is approximately normal.
(c): Calculate the probability that at most 67% of the people in the sample drink the cereal milk.
(d): Of the poll respondents, 67% said that they drink the cereal milk. Based on your answer to part (c), does this poll give convincing evidence that less than 70% of all U.S. adults drink the cereal milk? Explain your reasoning.