Hadey is planning a campaign to secure voting rights for the goats of Avocado Park. At the moment, 53% of the residents who are eligible to vote support the idea, but Hadey doesn't know that. He wants to assess the popular mood, so he selects a random sample of 47 eligible voters from the neighborhood and asks them if they support votes for goats.

Questions:

a. If you wish to use the binomial distribution to model the number of members of this sample that will support votes for goats, what must you first assume? Be precise. b. What is the probability that exactly 20 members of his sample support votes for goats? c. How many members of his sample would you EXPECT to support votes for goats? d. Describe the shape of the distribution of the variable "p-hat" representing the proportion of members of each possible sample of size 43 that supports votes for goats. e. What are the mean and standard deviation of the variable "p-hat" described in part d?