1. ) Two opposing opinions were shown to a random sample of 2,150 buyers of a particular political news app in the United States. The opinions, shown in a random order to each buyer, were as follows:

Opinion A: The issue of equal pay is more important than increasing the minimum wage.

Opinion B: Increasing the minimum wage is more important than the issue of equal pay.

Buyers were to choose the opinion that most closely reflected their own. If they felt neutral on the topics, they were to choose a third option of "Neutral."

The outcomes were as follows:

50% chose Opinion A, 42% chose Opinion B, and 8% chose "Neutral."

Part A: Make and interpret a 99% confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B.

Part B: The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?

2.) To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes had the extra donut and the shop owner claimed that one in seven boxes had an extra donut. Eight customers each bought one box of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut.

Part A:Is X a binomial random variable? Explain.

Part B:What is the mean and standard deviation of X? Provide an interpretation for each value in context.

Part C:Two of the eight customers buy a box of donuts with an extra donut. Is the shop's claim accurate? Compute P(X 2) and use the result to justify your answer.