The General Social Survey (GSS), conducted every other year, uses a random sample of U.S. adults to gather data on contemporary American society. One of the questions in the 2018 GSS was, “A doctor tells a couple that their genetic makeup means that they’ve got one in four chances of having a child with an inherited illness. Does this mean that if their first child has the illness, the next three will not have the illness?” Of the 1,170 respondents, 975 answered correctly. (What is the correct answer?) 

a. Identify the parameter estimated by the poll.

b. Verify the validity conditions for a theory-based confidence interval. 

c. Find a theory-based 95% confidence interval for the population parameter and interpret the confidence interval you obtained in the context of the problem. 

d. Is it plausible that 85% of all adult Americans would answer this question correctly? Explain how you are deciding.