A political organization with 100,000 members takes a simple random sample of 1,000 members and asks for their annual income in 2018. The sample average is $25,000, with a standard deviation of $20,000. 30% of the sampled members reported incomes over $50,000. A box model will be used to estimate the percentage of all the members in the organization with incomes over $50,000. Required:
a. The histogram of the incomes in the sample approximately follows the normal curve. Explain your answer.
b. The probability histogram of sample percentage of members with incomes over $50,000 approximately follows the normal curve. Explain your answer.
c. Calculate a 95%-confidence interval for the percentage of all members with incomes over $50,000.